@monkeyman1138: Do you also happen to have to use a 32-bit version of iTunes? I saw you saying you also use 188.8.131.52 which is their final 32-bit version. I'm starting to think this may be some kind of SSL/TLS version problem, where that version can't handle current https encryption anymore? The iTunes version is from 2015 after all, and the most recent version of TLS, 1.3, seems to be from 2018, so it may not support that.
Still find it really weird that a current version of Google Play Music can't download the podcast either, but if we both use the same version of iTunes and have that problem, that may at least be part of the problem.