[downwithdisease]

> I was a bit disappointed recently to discover that it doesn't offer a way to export data from it, which is pretty bad (i.e. your listening history and starred episodes, not your list of subscribed podcasts).

Maybe overlooked? Settings -> Import & Export OPML. Can't recall if it includes listening history and starred episodes but subscriptions for sure. This is the case for Android -- can't speak for iOS.

[vxNsr]

OPML usually is just your list of subscriptions, OP specifically wanted everything else, I don’t know of any app that shares that unfortunately.

[danhor]

AntennaPod offers a database export (and import). While not ideal, it's better than nothing.

[mkr-hn]

Overcast produces an export with everything, but warns they don't know of any apps that import it. The nice thing about OPML though is it's XML. An importer will just skip what it doesn't understand and import the subscriptions.

[Aissen]

Podcast Addict does that, you can backup the full app settings, and more than just the subscriptions/listened episodes. I'm guessing the format is specific to the app's export/import feature, but could be worked with.

[JulianWasTaken]

As the other comment mentioned, yes, this only contains a very short and not very useful list of the podcast subscriptions which if you have ~50 podcasts you subscribe to is easy to even manually resubscribe to, it doesn't have any of the useful data which isn't as easy to reconstruct.