I have had this issue for about a year.
I have downloaded podcasts on my laptop's itunes that I try to sync to my iphone but only two repeatedly load while the others won't.
When I plug the phone into the computer, it appears as though itunes believes all of the podcasts are already loaded onto the phone but I can't figure out why I can't access them on the app on my phone.
I've tried deleting all of the podcasts from the phone as well as the app itself but there was no change. I've also tried going into all of the settings on my phone and nothing seems to work.
I contact Apple a while ago and they said many other folks are experiencing this issue and to wait for IOS 17. I just downloaded it and there wasn't any fix.