I can't find Joe Rogan Experience, one of the most popular podcasts in the world, on Spotify, though I can find 10 related or similarly named podcasts. I'm not sure why they don't seem to have it.
Correct, Spotify apps can't play podcasts (meaning they don't support podcast standards like RSS, etc.). Instead, their backend ingests open web media and converts it for their proprietary platform. This allows them to "own" the listener/creator relationship, control what data the creators see, and modify the content to include additional advertising should they decide that's interesting.
Spotify does not monetize podcast content and likely will not in the future. My understanding is that they transcode audio to support all devices that the Spotify clients support, while being able to stream audio at a user-defined bitrate.
Spotify, for what it's worth, provides better analytics than most podcast hosts can provide because they also own the client. So by controlling the data that the producer sees, they're actually doing far better than the norm. They don't "own" any relationship any more than Apple Podcasts or Google Play (or any other pre-installed app) does.
Once you subscribe to a podcast in the Apple player, Apple’s servers are no longer involved. The app polls the RSS feed directly from the host’s RSS feed and gets the audio/video directly from the hosts server.
Every podcast out there is either in AAC or MP3. Every device that Spotify has an an app for supports both formats natively.
Apple also provides better aggregate analytics as of about a year ago.
Spotify does ingest RSS and MP3 files, but they rehost them from their own servers in a proprietary way. Some hosts have an agreement to "pass through" audio files, but the details of this are not clear.