I don't think this is purely a VPN problem. While I have VPN profiles installed, none of them are configured to connect automatically and I rarely, rarely use them. (I work in tech and I might use a VPN once every 3 months or so for 10 minutes to test something "remotely")
I have been working with Apple Support on what we think is an unrelated issue - my Passwords and Keychain iCloud sync wouldn't turn on. I would toggle it on, it would immediately toggle it back off again and no error messages were given.
In the process of tracking that issue down, I know that the Music Home Page issue doesn't go away after a reinstall of the Music app, using Reset Network Settings or Reset All Settings. It also didn't get better after I did a full erase of the iPhone and restore from a local encrypted backup. The problem persisted even after I removed all of the VPN profiles (as part of troubleshooting the Keychain issue).
The issue does go away when you turn off library sync. Before I realized you could click on a different tab right away when I would get "stuck" on the Home tab I would turn off library sync, change the tab, then turn it back on.
I'd be curious what people's music libraries look like that are affected by this issue and if that might be a contributing factor.
I have a music library dating back to 2002 and I was subscribed to iTunes Match up until 2021 or so, when I switched over to Apple Music. My library has a good deal of music ripped from my personal CD collection, most of which didn't match back in iTunes Match days but was uploaded since they were local/regional acts and/or live shows. I was very attentive to those uploaded tracks, making sure I had proper tags along with album art tagged into the files so that they would display properly on my iPod.
I'm wondering if this Home page bug in Apple Music has to do with people with non-Apple Music tracks in their library, since it doesn't seem to be affecting a large number of people and wasn't caught in beta?