1. Does this happen with all websites or only certain ones? If the latter, post link(s) so that we can confirm it.
2. Have you tried Safari while logged into a test account?
3. If you have a cable modem, have you tried resetting the modem? In my case, that has worked to cure strange situations but it has to be done while the computer is shut down.
macOS 10.15.6, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365