to discuss:
having a title attribute onto the prev/next buttons. Currently there is no generic next/prev i18n String

I'd prefer my original suggestion fwiw: that is, stick a simple select above it (and hide the other stuff from screenreaders).

a pro argument for the current solution: it is 0% JavaScript, just HTML+CSS

Perhaps. The CSS tortures radiobuttons into submission while a select would work entirely as it should with or without JS. But it's true that without JS the approaches would be competitive rather than complementary, so you'd have to hide one of the two.

I should clarify that from my perspective the main or only issues with that theme selector are that you can't browse through the themes with your arrow keys and that you're forced to go through them one by one. Also the focus is lost every time you click, while it should remain on the previous or next button.

In short, if you don't like the arrows I'd remove them completely instead, although I'd rather just keep it as it is and add a select to resolve the remaining issues. (I was planning to look into that this weekend if I found the time.)

Let's merge then, but additional simplification welcome