I do use their app but I’m pretty sure you can have your own RSS for audiobooks, and I’m assuming for podcasts too. I really recommend you give it a go :) let me know if you need any help, or just at the selfhosted community. Happy to help

Edit: just checked, yes you can have your own RSS with audiobookshelf, so you can still serve to your favorite podcast app.

If self hosting is your thing I use audiobookshelf to download the podcasts I subscribe too, has a nice interface to navigate them, and even mobile apps.

Not quite what you’re looking for (public archive) but a good starting point for a personal archive