Yes, it does offer importing from Trello: In a “project” (i.e. a collection of boards), after clicking the plus-button to add a new board, you can either just give it a name and create an empty board, or your can click “import from Trello”. I haven’t tried it, though, I’m not a Trello user (because why should I; I have Planka, haha). You can probably try out the import capability with their demo instance.

Have fun with your self-hosting adventures!

If I were to switch from Lemmy to KBin (or vice versa), would I have to start over (e.g. create a new account there and lose all my comments etc.)? Or would it be possible to “migrate”?

https://qwant.com

The closest free alternative to Trello would be Planka, IMHO. It works really well (rock stable, quick, painless), is pretty and doesn’t need much resources. The only thing I miss (which Trello also lacks, btw) is the ability to have subtasks in the way Jira allows them; for this, Plane or Leantime might be good candidates (I haven’t used either of them yet, though).