iOS 16.4 update causing issues with Apple Podcast app and my .m4a files

I recently upgraded my iPhone 14 Pro to iOS 16.4 and encountered an issue with the Apple Podcast app. I have a large collection of old Howard Stern shows in .m4a format that I listen to on the app. They've always played perfectly in the past, but after the update, they disappeared.

I managed to resync them with iTunes and got them to play again, but I found that if I close the Podcast app (swipe up), all the episodes are gone again, and I have to resync them. For now, the workaround is to keep the app open, but this isn't ideal since I use my phone for work, constantly switching between a barcode scanning app and a spreadsheet app.

I've tried restarting, reauthorizing iTunes, and deleting the app, but nothing has worked so far, except for a hard reset and reinstall (which I want to avoid). Does anyone have recommendations on how to fix this issue? Or should I just wait for an iOS update?

Alternatively, if you know of a good podcast app that can play .m4a files offline, please let me know.

Best regards!