Thank you!
1. 23.0.0.399/202111
2. Windows 11, 22621.1555 (happened with Windows 10 also), this is a clean Windows 11 installation.
3. Can be any site, it is random!
4. No
5. Premium
I have pinpointed the problem: I have Avira Premium installed, if I quit KSK or disable Avira's "Web Protection" feature everythings starts working as expected (it works both ways). The strange thing is that it was working fine a month ago and then suddenly the problem appeared. Please note that in my profile KSK is unrestricted (since I am the parent), a fact that makes the problem even trickier...