kdeconnect only request access to media in its permissions. While this maybe needed for the official play store upload do to Google's policies this is not needed for f-droid. I would like a un-resitricted version for F-Droid. Its not google's place to decide what I want to share and it shouldn't be yours either.
Looks like this something baked into Android 12+. Certain directories are prohibit from being shared in the that kde-connect does. These same directories are permitted for local access with the right permission flag. That is set in kde-connect. I'd say there's nothing to be done from kde's side.