iTunes is still <i>the</i> canonical place to post a podcast and get it picked up by nearly every app.<p><a href="https://developer.apple.com/library/archive/documentation/AudioVideo/Conceptual/iTuneSearchAPI/Searching.html" rel="nofollow">https://developer.apple.com/library/archive/documentation/Au...</a>
You can either use the iTunes API, or you can use the Podcast Index, which is free and open for anyone. podcastindex.org also has a number of APIs to help build a tool.