@sweetp I hadn't - and I accidentally discovered the right-click method, so all has been resolved now! This question is resolved.

I had to reinstall Cookie 6, or perhaps it was after upgrading to Big Sur (at about the same time), but Cookie now has thousands of favorites for the browsers that I use (main browser Brave, but also Safari and Firefox). I have NO favorites at all times. Unchecking them takes 8,000 clicks... How can I remove them all at once?

When I delete the favorites file from /Library/Containers/ etc they simply return.
Any advice would be appreciated.

That file did not exist, but files with the same name but a temp ending did. Renaming one did not help.
But then I deleted all (app, container files) and reinstalled everything from scratch and noticed the file ~/Library/Cookies/Cookies.binarycookies did not exist.
Thought once, then opened a website in Safari - and the file came into being. I immediately had Safari enabled.
The file is indeed the crux and it is created by actually using Safari.

The nuclear option still does not resolve the issue: Safari cannot be enabled.
Brave and Opera had no problems, Firefox was helped by the nuclear option.
I mainly use Brave, but airdrop always requires Safari, and some websites require Firefox to be used.

Just did the set-up again - now I had the option to uncheck websites.
It remains odd that I cannot do that later, but at least they're gone now.
Problem solved.

Just upgraded from v.5 to v. 6. This is what I see: greyed out favourites.
Interesting to see Facebook here: I quit Facebook almost two years ago.
Control click does not do anything.

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I do not want any favourites - none whatsoever. But I cannot undo them in Cookie 6. How do I do this?