Podcasts started out as distributing MP3 files; back then iTunes was a great podcast app (and music and audiobooks, and voice memos and more -- it was a glorious app before the fall.)
Over the years Podcasts really shifted to streaming, listen once, don't keep. Then, somewhere post Mojave (Monterey) Apple orphaned the physical podcast files stored in iTunes. The Finder shows physical files in your media library but neither Music.app or Podcast.app can browse them. Music. app's browser Get Info still shows the media type dropdown, but there's only one type! (Music)
If you click on a podcast file iTunes will play it and import the file into the media library where it has media type Music but genre podcast.
So the fix is:
1. Move Podcast folder out of media library
2. Reimport all podcast as music.
3. For genre podcast multi-edit to make more like podcasts. You use macOS Music.app column browse to see all with genre "podcast", select all then hit cmd-I. You'll see a prompt asking if you wish to multi-edit (yes). Then in Options select: 'remember playback position' 'skip when shuffling'. I think this operation may fail if a file is being uploaded to Apple Music (at least I get to burn GB of Apple Storage!) so let uploads complete if it doesn't work.
PS. Voice Memos are supposed to have a migrate path, but that didn't show for me.