Do you just use podcasts on your phone? If you have an Android phone, AntennaPod, while not self-hosted, works very well and is FOSS. There are other options to "self-host podcasts" to varying degrees:

• PodHoarder: mentioned in another comment, which could be piped into AntennaPod, but I find that a bit redundant for me

• AudioBookshelf: a fantastic self-hosted audiobook server, and an okay podcast server, but is focused around streaming from your server to your listening device, and I prefer to download on wifi to listen later (it was pretty clunky for that workflow).

• GPodderSync: barely supported at this point and missing too many features to be useful in my opinion, but a neat backend for AntennaPod and other players to sync to some degree.

Bonus: the creators of AntennaPod and other FOSS podcasting software are working on a replacement for GPodderSync here: https://github.com/OpenPodcastAPI

EDIT: for RSS in general, I use FreshRSS, which uses the g-reader API to sync across multiple apps. It's awesome.

I currently use AntennaPod with NextCloud's version of GPodderSync; which is...adequate.

My ultimate solution would be one where a self-hosted app that tracks and download my podcasts, and then proxy them with some sync mechanism to an android app, but keep them as separate shows with artwork and stuff rather than consolidate them into one feed. I could then choose to listen on the self-hosted web interface or the Android app, and they would be kept in sync.

Why do you need to self-host a dedicated server? Just put AntennaPod on your phone.

I am really happy with miniflux. It supports mobile and has good keyboard navigation support on Desktop. It's also runs really smooth on my rather low powered homeserver (rpi 2b).

For push notifications you can use a simple script with ntfy. For example miniflux-ntfy.

If you're just looking for RSS -> Push take a look at feedpushr

I use it with gotify without too many issues.

I'm interested in seeing what you come up with.

Does something like podHoarder fit the bill?

I tried a few.

Podhoarder is nice but more geared toward hoarding and a bit complex for listening.

Podfetch is nice and currently maintained but has some issues with proxy auth. It might cut the cheese for you I think. It has a weird naming scheme on disk tough.

AudioBookReader is amazing and still currently under very active development. With its mobile app is perfect for my use case. Podcast support is just fine for me.

PodGrabber seems abandoned since 2022, but I didn't try it.

Not sure if it meets your needs but I’ve been using Audiobookshelf for pulling podcasts. The default web interface is simple and straightforward and you can create secondary rss feeds if you have another podcast app you prefer. Has apps for iOS and android, though the iOS app is TestFlight. As a podcast player it’s decent. Not sure if it does notifications, I tend to disable them.

I started using it because one of the podcasts I listened to ended and I wasn’t able to go back and relisten to the episodes. Decided to start archiving the podcasts I was interested in.

For podcasts I recommend audiobookshelf. It has a very nice podcasts category with ability to backup the podcastst yourself, also syncs progress over multiple devices.

For rss I use miniflux.