No, it actually doesn’t make sense to store it in any kind of profile.
You are right that some fly by data might end up in a server log somewhere but those aren’t kept around for long...if they are kept at all at Facebook scales
Storing and computing data is very expensive and risky at FB scale so they will only keep around what they actually need for as long as they need it. Meaning that data gets send to the server, gets aggregated and then deleted.
An exception of course is content generated by users such as a newsfeed post, as is the nature of the product that content stays around until users delete it