it doesn't correlate across sites by default -- the reasonable definition of a 3rd party tracker. by your definition, everything not complete self-hosted is a 3rd-party tracker. eg, netlify, which uses server logs to "self"-analyze would be a 3rd party tracker. it is not self-hosted and the data is stored elsewhere.

some might add: for the purpose of resale of the data, but I don't think that's a requirement to be classified as 3rd party tracker. the mere act of correlation, no matter what you then do with the data, makes you a 3rd party tracker. in case you think that's just semantics, this is important for GDPR and the new california law.

you can turn on the "doubleclick" option, which does do said correlation and tracks you. but that's up to the site to decide. GA doesn't do it by default.