I don't know that Google gets to log your access in that scenario, Plex is just using their login system.
Plex sure does know, though, whether you log in via Google or not, so "I don't share videos using google to log in" is still a bit of a weird statement and not the reason you'd be worried about your piracy habits.
Incidentally, if a friend or family member is hosting a service and "tells me these are the options to sign in to the service I'm hosting" I'd tell them to go away, which is something my own relatives have done to me a bunch when my proposed self-hosted alternative isn't perfectly smooth and just as convenient as the corpo alternative.
Not surprisingly, the only two selfhosted things my family has ever used are Plex and Home Assistant.