I think it's possible to do. Basically all it needs is the audio files, a webserver and some RSS/XML.

Here is a description how to write the XML part. http://www.podcast411.com/howto_1.html and https://resourcecenter.odee.osu.edu/digital-media-production/how-write-podcast-rss-xml

As you can see the actual link to the mp3 (or ogg ?) file is enclosed in the "<enclosure url=" tag.

So i think you could upload the files to Commons, like you said, and then put the XML file(s) on a misc webserver.

Theoretically any existing shell user could put it on people.wikimedia.org but i assume you'd want a "nicer" URL.

For example we could put it on "bromine", a VM in production that hosts some other "microsites" (./modules/role/manifests/microsites) like the annual report, transparency report and the endowment site.

It would mean that we setup a minimal Apache virtual host once and then you'd be expected to upload the XML files to a repo via Gerrit when you want to make changes.

I think it does probably make sense to host the podcasts themselves on Commons, and then just set up a simpler microsite to host indexing (RSS/XML and some nice indexing for human browsers, perhaps?) like @Dzahn says.

For existing examples on commons of podcasts in organized sets (which can be directly linked from the RSS/XML and the microsite in general):

https://commons.wikimedia.org/wiki/Category:Podcasts
https://commons.wikimedia.org/wiki/Category:This_Week_In_Palestine;_comparison_of_Israel_and_Apartheid
https://commons.wikimedia.org/wiki/Category:FM_radio_programmes

When viewing a category on Commons, there's a link in the sidebar titled "RSS feed", linking to a feed of that category, generated by the CatFood tool hosted on the Toolserver. It can also generate RSS feeds of uploads from a particular account.