How many humans will actually see my US tax return?

I don't think the IRS publishes much of their internal process anywhere. But they do have pages on your rights as a taxpayer and what to expect if you're audited. That to say, most people are guessing that:

If you e-file, then I would expect nobody actually looks at your return unless you are selected for a random manual review or your return is well outside the statistical norm.

If you paper file, then some data-entry person enters your numbers into the computer system and it gets analyzed through the same programs. They don't actually check any numbers.