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”?

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).