https://wafflegame.net/daily has the colours from Wordle but instead you start with all the letters for several words and have to swap pairs of letters until they're in the right place.
edit: I've only just noticed that this is a BestOf post, not your own question 🤦‍♂️
There's a British quiz show called Only Connect that finishes with essentially this puzzle, except harder (with plenty of red herrings), timed but unlimited guesses until you have your first two groups, and extra points for naming the connection (even ones you failed to find).
We play NY Connection like we have to figure out the connection before entering the group, but we often end up with a final set of four that we just have to assume is some American references like NFL teams (like yesterday).
I feel like I’m missing something with Connections. Like, the conceit of the game is that there are multiple potentially valid groupings and you have to figure out the right ones. But I always feel cheated when I guess seemingly valid but incorrect groups. As if I’ve lost a “guess what I’m thinking” game, not a real puzzle.
You know, there have been a few times I've thought that, but you need to think of the 16 word puzzle as a WHOLE. Even if your group DID work, would the other three groups still make sense?
They commonly use similar words in different groups to throw you off the right track. So, it's not "guess what I'm thinking" it's more, they already know what you're thinking, and what other ways can we group these things?
Semantle, maybe. Guess word, and your guesses are rated based on the similarity of the meaning to the meaning of the target word. It does take a long time, though, to complete a game