Has my browser been infected after visiting malicious link?

Today I typed in a URL of a site I know. Unfortunately I missed one letter of the TLD. I typed .co instead of .com. No problem, I'll quickly retype the URL. Unfortunately, this was not possible. The URL bar kept being reset because the page forwarded me over and over again. Ultimately I just closed the tab, because it was clearly not a benevolent website. An hour later, I noticed I was logged out of Messenger. I didn't think anything of it at first, but shortly after I noticed I was also logged out of Google, Youtube, Stackoverflow, .... all my accounts. I started getting suspicious at this point. A quick check in the settings showed that all my cookies were still there. I cleared them just in case this last website injected something maliciously. Now I wonder... * Is this a pure coincidence, or might this strange website have got something to do with me being logged out of everything? * Is this even possible? I'd think a website should not be able to access this kind of stuff. * Is there still a risk of my browser being infected after me clearing my cookies? * If applicable: what's the purpose of this "trick"? Letting me log in again, so a keylogger can catch me password? Something else? FWIW: I use Firefox 110.0 on Arch Linux. Thanks!
http://dlvr.it/SjY3nV