Please do yourself a favour and download a proper podcast client. There are so many great ones out there, they’re often from independent developers, and podcasts are one of the last parts of the modern web that actually work how the web was supposed to work: decentralised* and open access. Don’t let media giants turn it into a closed system.
* the elephant in the room being that the iTunes podcast directory is the de-facto standard index. It’s freely available, but the fact that it could be withdrawn at any time is not great. Projects like https://podcastindex.org/ are trying to address that.
I agree with you, I've just struggled to find one that worked well on Android but also synced to desktop. I'm on iOS now, so maybe it's time to look through the options again.
* the elephant in the room being that the iTunes podcast directory is the de-facto standard index. It’s freely available, but the fact that it could be withdrawn at any time is not great. Projects like https://podcastindex.org/ are trying to address that.