This is just a wild ass guess but your symptoms and solution are describing a problem with DNS over HTTPS (DoH) which is a feature of Private Relay to encrypt your DNS queries). It only effected Safari, and it was fixed by messing with DNS settings.
(That is in DNS settings in Network settings)
Again a guess, you might not even have Private Relay or maybe its not turned on.
However if it is it could be 1 of 2 things.
One, you were on a public wi-fi that had a login portal which DoH doesn't play well with by its very nature.
Two, a fluke with DNS. Happens with encrypted DNS on occasion.
Three, Verizon blocks the port is uses (443 I believe) when tethering. The reason they would do this is because tethering is highly policed, monitored and limited, 15gb before your throttled on Verizon I believe? DNS queries tells them what you are doing. But if they can't see your DNS queries they can't throttle your internet speed when your using a service thats heavy on their network, mostly streaming services.
They do claim their DNS servers block malicious attacks (DNS poisoning) and provide better service by load balancing. Its hard to overlook how they conveniently leave out they lose a lot of control of what you are doing on their network though....suspicious even.
Unfortunately I dont have tethering to test this out but if you do have the feature see if you can enable it in Settings > AppleID > Private Relay (beta) and Safari's preferences under the privacy tab...
And see if you can enable it in Network settings under you phones tethering connection...
Then test out Safari again. I'm assuming it was a fluke but some mobile telco's are blocking Private Relay, T-Mobile I believe so I wouldn't put it past Verizon to block it where they use DNS queries on a regular basis.