Did you restart your phone while you were testing?
Maybe this debugs the issue.
In my experience, VPN connections bug from time to time.
This issue appeared in my time before (must have been Android 11 or something like that on an OnePlus device) and with GrapheneOS up to the current version on my Pixel 7.
If I switch off airplane mode, the VPN seems established but there is no network access at all; just manually turning the VPN off and on again helped with it immediately.
Same behaviour appears when I unlock my Private Profile, roundabout every tenth time.
I have always been using Wireguard.
If the VPN button of Android itself bugs, I switch to the Wireguard app to turn it off/on but sometimes even this bugs for seconds.