Why were gold and silver treasured in the mercantile ages when they weren't very useful?

Unlike every other metal known since antiquity, gold doesn't tarnish or oxidize or decay. It's the very embodiment of purity and immortality. It invokes the divine. If you make something out of gold and you keep it safe, it'll look pristine indefinitely. This also makes it great as an offering to (the) God(s).

Silver tarnishes, but very slowly and can easily be polished to a mirror finish. This makes it well suited to make "nice" things where gold isn't necessarily appropriate or cost-effective, and it can be added to gold to bulk it up and improve its material properties without ruining its luster.

Copper tarnishes quickly and forms a green patina in salty sea air, and the vast majority of ancient settlements happened to be on the coast. It's still a useful metal, but it has to be kept up, a constant reminder of one's mortality. It's more suited for tools and cookware than as an offering to God.

Rarity helps a lot with this too, of course. It doesn't matter how immutable gold is if you can just find it anywhere. This also means it's great for turning into coinage with your face on it, to remind everyone exactly who's in charge.

Once upon a time, pure iron used to be even more valuable than gold. Before we learned how to smelt it, pure iron was extremely rare, and the only pure iron that could be found on or in the Earth's surface came from the heavens (meteoric iron). Finding a pure chunk of iron was tantamount to winning the lottery.

The same goes for aluminum. Despite being one of the most abundant elements in Earth's crust, pure aluminum almost never occurs naturally. In the 19th century, people had cutlery made out of aluminum because it was fancier than silverware. It only dropped in value once we started to refine it on an industrial scale, which involves electrolyzing molten alumina, requiring an immense amount of power.

Long story short, value is relative. Iron and aluminum got cheap because we figured out how to make more and more of it. Gold and silver remain precious metals because they only got rarer and rarer as more people went looking for them, and their value only went up as we started finding practical uses for them.

No no it wasn't just a shiny metal. Silver and gold were (still are) noble metals, and that means they are more inert than other metals, and by inert I mean "it doesn't rust or tarnish". Silver sometimes tarnishes, but gold is very hard to tarnish.

And you may think, so what, big deal, it just saves time polishing metal. Right? No, if you ever ate from a brass or any other alloy metal cutlery/plates, you will remember the absolutely horrible bitter taste these metals have. You pretty much have to hard scrub and polish each piece daily to avoid getting that taste. Tarnished silver otoh, doesn't taste as bad. So not only it takes longer to tarnish but even if it does it gets a pass. Bear in mind stainless steel and plastic weren't really a thing back then, so you'd be stuck with metal or wood for cutlery.

But wait, there is more. Both silver and gold are particularly malleable and ductile; this means you can hammer them, beat them, bend them, and spin them into very thin threads and the metal won't break as easily as other metals do. I've worked as a silversmith so I've experienced this first hand. Working brass into shape and adding ornamentation to it is very hard, you need to anneal it constantly and use more force. It cracks more easily while you work it too. Copper is slightly better, but silver is way ahead any of them, and gold is just like working butter. There is no comparison. Much easier, really good results. Also gold has a slightly higher melting point than silver, meaning it's somewhat easier to solder.

All this makes gold and silver the only fitting choices for fine jewelry and luxury items such as silverware, trophies, embroidered clothing, etc. And these items signify wealth and status, so, obviously, this made gold and silver very valuable and useful back in the day.

I think it's like this:

Due to their rarity, gold and silver are only available in limited quantities. This makes them suitable as a means of payment, as the limited availability of these materials allows them to have a relatively stable exchange value. They are also durable and easy to work with. So as a means of payment, gold and silver became representative of goods that can be purchased with them.

Coins made of gold or silver, which were used as currencies early on, were not very forgery-proof. However, as the materials themselves are rare, good forgeries were only possible if the material was available. And the rarer the material used, the more forgery-proof the coin became, which is why it made sense to mint coins with a high exchange value from rarer materials (bronze or copper for lower value coins, silver or even gold for coins with higher exchange value).

Early examples of inflation illustrate quite well how value and material are linked: In ancient Rome, for example, silver coins were used as a means of payment. Under Emperor Gallienus, there was massive inflation because he had the silver content of coins reduced to below 5% in order to finance military campaigns and other expenses (he basically created value out of thin air with this move). This ultimately led to a loss of confidence in the currency and thus to a decline in the value of the coins, as they were not inherently forgery-proof (it became quite easy to mint counterfeit coins with such a low silver content).

Still, the value of the material itself has always been variable and depended heavily on its rarity: When the Spanish imported large quantities of silver from their colonies in South America in the 16th century, the value of silver fell because the material became less scarce. This eventually led to massive inflation throughout Europe at the time.

However, the value is not so much determined by the material itself, but by the value that people ascribe to it at a certain time. There are also great historical examples of how speculative bubbles work: In the 17th century, tulip bulbs were at times traded at enormously high prices in the Netherlands because they were difficult to obtain and therefore rare - this made them coveted as a status symbol. However, this bubble finally burst in 1637 when traders could no longer find buyers due to the astronomical tulip bulb prices - demand was covered; the "Tulipmania" had ended. As a result, the merchants began to sell these tulip bulbs in "panic sales" at ever lower prices in order to recoup at least part of their investment. As a result, the price fell to near worthlessness.

Such speculative bubbles still exist today, of course. This is demonstrated very impressively time and again by cryptocurrencies, for example, which are not even material and have no central regulatory authority (such as a central bank) - their value results basically just from what someone is willing to pay at a certain point in time.

So gold and silver were and are valuable not only because of their utility value, but also because of their use as a means of payment, whereby the value - as with today's currencies - results from a (more or less stable) consensus on the exchange value in goods attributed to a material or currency.

As gold in particular has historically been used as a means of payment for a very long time, most countries still have gold reserves to back their currencies to a certain extent, even if their currencies are generally no longer directly linked to an equivalent value in gold as they used to be. Nevertheless, the US, for example, still holds large amounts of gold at Fort Knox and elsewhere to counteract the fact that paper money, and especially its virtual equivalent in some digital form, is materially worthless.

It looks good. Every culture that's found gold has made jewellery out of it. The rest follows from there.

It doesn't tarnish, so once you've already decided it looks good, you then notice it doesn't age or spoil like pretty much everything else. That gives it a magical aura and allure.

It's fungible (consistent and exchangeable).. gold here looks exactly the same as gold there

It's malleable - can be easier subdivided into units for exchange. Can readily be worked into attractive decoration.

Although it's rare this isn't what drove is attractiveness (the Inca had abundant gold and still chose it to make jewellery out of, it just looks better, even if there's a lot of it), but scarcity did help it become a reliable store of value across the middle east, africa, asia and europe.

It was valuable because enough people accepted that it was valuable. It's really that simple. Our money is backed by "the full faith and credit of the US government". What is that really worth?

One of the answers is colloidal gold. It was not just a shiny metal, it was used for many purposes, including drinking water with microscopic specks of it (as weirdly as it sounds). According to Wikipedia:

Used since ancient times as a method of staining glass, colloidal gold was used in the 4th-century Lycurgus Cup, which changes color depending on the location of light source.

During the Middle Ages, soluble gold, a solution containing gold salt, had a reputation for its curative property for various diseases. In 1618, Francis Anthony, a philosopher and member of the medical profession, published a book called Panacea Aurea, sive tractatus duo de ipsius Auro Potabili (Latin: gold potion, or two treatments of potable gold). The book introduces information on the formation of colloidal gold and its medical uses. About half a century later, English botanist Nicholas Culpepper published a book in 1656, Treatise of Aurum Potabile, solely discussing the medical uses of colloidal gold.

Edit: it's worth mentioning that it's not so weird to imagine if we consider that our diet requirements include many metals, such as copper (important to the hair), zinc and, especially, iron which composes our blood (even though it's a different atom of iron than the iron from metallurgy, it's "iron" anyways).

It's not useless, before stainless steel it was one of the few inert metals that could be used for food handling.

Aluminium used to be more valuable than gold, Napoleon had his most honoured guests served food on aluminium plates, while lesser guests had to make do with solid gold.

I do not have the time to explain the entire labor theory of value to you so you'll just have to trust me when I say that the labor required for extraction enabled gold and silver to possess a value abstracted from how they can be used. This is known as exchange value and it can only be measured when 2 commodities are prepared. exchange value is quantitative not qualitative so an expression of exchange value looks like: 20yds of linen = 1 coat. This is only true in a society if it takes the same social labor time to produce 20 yards of linen as it does to produce 1 coat, only then are they exchangable. It is the labor that gives them value. So then it may become obvious that having a universal commodity to compare everything to would be useful. Gold fulfills this role well because it is labor intensive to produce (high value due to labor time required), it can easily be divided into smaller and smaller parts to more adequately express precise values, it is rare, and it doesn't tarnish. Silver is similar but not as rare and tarnishes quicker, both work though.

Copper is abundant and tarnishes quickly

This is just speculation so not a real answer: many precious metals are easier to work than some of the harder counterparts like iron and steel. Secondarily, it's harder to fake those. Even if you make an alloy counterfeit with the same weight when coated with the precious metal, you still need at least the previous metal and it would still fail other tests such as malleability.

Scarcity.

Copper and bronze were common currencies, though. Both as metals and in coins.