I'm having the same issue here. It's only broken in Safari (and possibly other Apple apps). If I open Chrome or Firefox, web sites load fine.
Can you try the same? See if the issue is only in Safari.
No idea what the "fix" is, but it's obnoxious and driving me bonkers.
Edit:
I've ruled out Private Relay, it's turned off.
I've ruled out the new Wifi Private Wi-Fi Address thing as it is turned off along with Limit IP Address Tracking. However, this feature is turned _on_ at my parents house and I don't believe the issue is happening there, just my home network, which is all Ubiquiti based with an EdgeRouter and a Unifi access point. At my parents it's just a bog standard consumer wifi unit from DLink or something like that.
I have forgotten the network multiple times and re-joined, no changes.
I also do not have any ad-blockers in the browser, just 1Password and Save to Readwise. Though at home I do have a Pi-Hole setup. So I guess that's another avenue of testing I can do.