Auto-downloads work wonderfully here and can even be set per-podcast which is such a nice feature.
Not saying this to denigrate your experience but to perhaps soften the ‘is horrific’ notion into somewhat more of a ‘does not work for you’ one. Otherwise, I suppose Pocket Casts is also open source nowadays - or has always been and I did not notice? But that was a reasonably good alternative for me as well before I switched to AntennaPod.
That is a little of how I use it too - I have all podcasts set to download automatically globally (set it up to 25 episodes at the same time) and put them in my queue so I always have exactly 25 episodes to listen to in any order there each day.
Then there are 2 daily podcasts that I do not let automatically download (but automatically refresh, and I love that the app delineates between the two), however one regularly produces longer episodes including a lot of the shorter ones that I do let it automatically download. Huh, I never realized how advanced the setup actually is. Though I do remember the actual ‘setting up’ being relatively painless after getting to grips with the global/per-podcast difference.
Also, fwiw I have the synchronization set up using one of the self-hosted options instead of the default gpodder service - which is often down intermittently - and it works well enough, even if a bit slow every now and again.