'Rendered item' processor renders in the admin theme if indexing is done either on node edit or from the Search API UI

Oh wow, that does look very easy, thanks!

Great job, thanks a lot!
It looks so easy when someone knows what they're doing …

This needed a re-roll, though. Also, while it's awesome that you included proper DI, we normally also add getters that automatically default to using \Drupal for the injected properties. At least for consistency's sake.

Finally: is there maybe an easy way to verify in the tests that the theme is indeed being switched? Either through the output or by trying to catch the code at some point while it's in the other theme? That would of course be great to avoid regressions later.
But we can also skip it if it's too much trouble.

In any case, again, thanks a lot!

Re-roll, plus a tests-only patch to see whether the existing test doesn't suffice after all. (The comment suggests as much, at least.)

Awesome!
Thanks also, Joris, for reviewing!

Committed.

Thanks a lot again, Lee, for providing the solution!