To answer your question the way you meant it, no. You can use Spotify on a mac or iPhone/iPad and then set the AirPlay output device to the homepod, playing Spotify music out of them just fine. I literally do this every day.
No, you're stuck with handoff or airplay.
You can't link Spotify to it? What does the voice assistant on a speaker do if not "Siri play Shooting Star by Bag Raiders"?
Surely you can link Apple Music?
I'm like 90% sure that's on Spotify. Apple opened up APIs to do this and Spotify refused to do it because... reasons.
The reason is that Apple wants a cut of the Spotify subscription money when users sign up for Spotify on an iOS or iPadOS device. IMHO, it's a bad look for Apple. They should either get out of the music business or stop taking a cut of the money from apps that compete with Apple services.
Do you have a source for that? As far as I'm aware, that has nothing to do with it -- e.g. Spotify is allowed on iOS as it is.
I haven’t looked into it in a while. I guess it changed between 2019 and 2021.