The fallback assumed a single `Default` profile, so a browser whose cookies
live in `Profile 1` reported nothing to import — and since sources without a
cookie database are now left out of the menu, it disappeared entirely rather
than degrading.

The user-data directory is scanned for directories that hold a cookie database
instead, which is the same signal the install check uses.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>