Similar-sounding problem on my iPhone 13 Pro Max; iOS 15.2: no beta versions. The problem that has persisted since September, at least.
When browsing the web, Safari occasionally will return ‘cannot load page; not connected to the Internet‘. Seems to occur at random times. WiFi is strong and stable.
Hitting refresh will cause the page to load normally, but that is such a kludgy fix, and it is annoying.
It happens most frequently with my Linksys router, but also on an Eero 6 mesh network. It also has happened on an older Apple airport that I turn on occasionally. No hard data on the airport, but my perception is that it happens less often on the Airport.
The airport WPA group key interval is set to 60 minutes; which is the default. The Eero GTK interval is set to 3600 seconds. I don’t remember seeing either in the Linksys interface; the router is a few years old, and I am older, so I may have missed it. From a network security perspective, though, setting the interval to zero sounds like the wrong way to fix this (haven’t tried that and don’t plan to)