Google data never leaves their platform, it’s too valuable to them. Retargeting works the other way where a site or app attempts to get a cookie or fingerprint and gives them to Google or Meta to target that user with ads

IIRC not to Meta themselves but to Meta's customers (I mean, the advertisers, which are the ones who pay. You the user aren't Meta's customer, you are their product) but it's been a long time since I hear Criteo's technical pitch so I don't remember how it works.