Certainly, a farmer manually collecting bull semen isn't engaged in sex work.

But I would say at the very least "sex work" covers dominatrices, pre-recorded and live-streaming porn performances, strip club and lap dance performances, as well as escorts. So "sex worker" isn't precisely equal to "prostitute"

The objective of fertility work is sperm/egg/embryo/whatever, not orgasm. If they could efficienctly stick a needle in the gonads and extract the reproductive cells, they would.

Strippers are sex workers, but most of them aren't trying to make their customers orgasm. At least, not in the moment.