Unemployment comes from surveys (the CPS) where they call people and ask if they're employed. So the answer to questions like "do Uber drivers count as employed" is, it's up to them.

There's other questions about full-time or part-time, or multiple jobs.

(Multiple jobs are interesting because you'd think they'd belong to overworked underpaid poor people. But they're not really associated with that, and they go down in recessions since that's when you have no jobs.)