It was extremely unsettling until I realized what they were doing.

They replace the ad breaks that would normally be in a podcast. (Like when the hosts say "we're going to take a quick break to talk about our sponsors for this episode"). It's not an unskippable ad like you get when listening to music using the free tier. It's inserted directly into the audio stream.

Edit: I guess it's possible the Conan podcast is doing that somehow and not Spotify, but I've never had something like that happen when using the Apple podcast app.