What does a CTO actually do?

Don't know why but for some reasons I cannot take people seriously that write articles about the importance of their role.

In the media, CTOs are often portrayed as tech geniuses or wizards, single-handedly coding complex algorithms or inventing groundbreaking technologies.

Not sure what kind of media the author of this articles (op?) consumes, but I don't know anybody who thinks something like that.

Somehow I get the sense that humility and authenticity aren’t required skills

This is a bit of a narrow view of a very vague term. Having worked with many different sizes of organisations i can say that the responsibilities of whomever is labelled CTO are completely arbitrary. The only thing you can establish is that they are the person accountable for the technology decisions.

Sometimes that's a legacy developer, sometimes that's the first sys-admin.

Sometimes it's the VP of engineering.

Sometimes that's the person that maintains the best relationships with software vendors.

Sometimes it's the person that was hired externally to explain the tech to the CEO and let's them make informed executive decisions.

Sometimes it's just a public figure used to promote the org and maybe do DevRel.

Sometimes it's the Architect that designed the ecosystem.

Sometimes it's the ancient programmer that has kidnapped the entire codebase so that no-one else can sanely work on it.

Sometimes it's a six sigma type that setup the ticketing system, PRs and the release process.

At any size, the CTO is whatever the org needs him to be at that point.

That first paragraph is basically my job now, except for the investors and clients part. We have an actual CTO so he gets to deal with all that crap and I can focus on the tech stuff.