How can I export my local databases via Local Network Transfer (LAN) only?

This is actually possible but not very intuitive at the moment.

First, you’ll need to make sure your databases are visible to Files (i.e. in the Strongbox Documents folder). You can do by sliding left on your database and tapping ‘Show in Files’ if that option is there.

Next, tap the + button and select Add Existing, then select Transfer Over Local Network. Go to the indicated web address on your laptop/desktop and you will be able to download/export as well as upload/import.