I used to have a serious podcast habit - one of which used to run adverts for Audible. Now I listen to audiobooks and hardly ever listen to podcasts and never listen to the podcast where I learned about Audible.
When it comes to Audible literally anyone can be 'sponsored' by them - I don't know if the big guys get an upfront or set amount but I was able to register as an Audible podcast affiliate before we even had a single episode out
I know that with Squarespace at least podcasts with a larger listenership have a completely different deal than the regular affiliate marketing channel- though I don't know any details. I kind of assumed it was the same across the board for podcasts on larger networks though I don't really know for sure.