Yeah, me too. At one point a few days after installing Catalina on my work laptop I think I accidentally clicked on the not-before-seen "Podcast" icon on the dock, I think that may be what started it. Why does anyone at Apple presume I want podcasts? Are people in general too blank to figure out on their own what they want to use their computers for? OK, so set up a bunch of potentially interesting default stuff on a brand new, fresh install, but don't change my UI things around on an in-place upgrade.
Thing is in this case, I absolutely don't want to connect to Apple Media Services. There is no [ Never ] or [ Cancel ] button, just [ Later ] and [ Apple ID Preferences ]. I just tried clicking [ Apple ID Preferences ] and tried the [ Sign Out ] button. Let's see if that helps - I suspect it won't.
Burying the user-desired outcome amongst a bunch of misleading paths makes Catalina act more like MALWARE than anything else.
Interestingly, I use a PC for most of my work and while Microsoft seems to get a bad rap, I am able to get Windows 10 into the state I want a lot more thoroughly and permanently than macOS.
-Noel