This repo has a python script that generates an RSS podcast feed out of the Spoken Wikipedia project files, using this page as the data source. The generatepod.py script creates (to stdout) an RSS feed of the Spoken Wikimedia Project files. There are a few recorded files that currently don't make it -- some have not been transcoded from ogg to mp3, and a few I think I have some special characters that aren't being handled right in this script.
A copy of the generated feed is at https://wcast.me/sw
It should work as a standard RSS feed in any podcast app that will let you enter one. So far I've only tested it in AntennaPod (Android only), Pocket Casts (Android and Apple; just put the URL above in its search bar) and Apple Podcasts. AntennaPod works slightly better since it shows images for individual episodes and has better search and filter functionality, which helps when you're dealing with 1600 episodes.
(0) Download (if necessary) and open AntennaPod (1) tap the three-line menu in the top left, (2) tap "Add Podcast", (3) look down under "Advanced" and tap on "Add Podcast by RSS address" and (4) paste or type in https://morris.cloud/spokenwikipedia/
It's a big podcast -- 1600+ "episodes" as of Feb 2023 -- so it will take a few seconds to open up. Click "subscribe" and you should be on your way. My next plan is to add to the script, or make another one, to download and convert the files to mp3, which be a more "normal" podcast that would work for most users and could be submitted to podcast feed listings.