"Have you noticed any sites that don't work properly or work differently than for someone not on a VPN?"
Much moreso when I was using a 'free' VPN years ago (for obvious reasons).
With NordVPN, on very rare occasions, I have to disable it.. usually for online transactions (which is also understandable).
I signed up with Truth Social today so I could 'follow' Pres. Trump, and it had a page that refused me to go past it, I believe because of the VPN (on the PC).
Ironically, on both my iPhone and iPad, which both also use the same VPN account (but more than likely each using a different VPN IP), the registration went smoothly and quickly.
One issue you can run into is that with a VPN, you may wind up assigned an IP
address that was already used by someone else to do something ban-able, or
worse, and THAT will be the cause of your failed registration attempts and such.
(Using a VPN supplied ip address previously banned for someone else’s activity.)
When that is the cause, reconnecting to get a different IP can often let you proceed.