[lxgr]

Is that actually what's happening?

Why would Google need this information? Don't they already get all of that and more in the queries themselves?

Or is this about supplying Google with a user profile that persists beyond incognito tabs, cleared cookies/history etc.?

I read it more as "we, Mozilla, want to know what Firefox users use their browsers for" rather than "we want to hand this data to Google on a per-query level". That said, it is incredibly vaguely worded.