There's a few ways first party cookies can track you. Probably the biggest single way is Google Analytics which by default uses only first party cookies. Even without cookies at all, GA could track you across the web although first party cookies do make this a little easier and "better". However, first party cookies can help trackers in other ways like for CNAME cloaking[1] which basically makes a first-party cookie function similarly to a third-party one.
Disclosure: I work for a small privacy focused ad company.
> If I get logged out of every website on a weekly basis I'm going to be annoyed.
Then those websites should move to Passkeys.
> How do they use first party cookies to track you?
Because Meta and Google allows websites to submit advertising data to them server side using a self-hosted JS file which sets the first party cookies on your behalf.
