I guess it also has access to the cookies for all your logins.

Yes, it has access to the internal storage mechanisms of the browser.

I used to use Cookie Auto Delete for years. But when I last checked it seemed unmaintained. I log out of all somewhat important services anyway every time I am done.

For important stuff like banking I use Firefox containers.

Yeah, all of them could have their weaknesses and vulnerabilities. I just hope no attacker hits exactly the stack I use...