Ackshully, you would need an appropriately rated pilot for return to
service. You'd need an IA to approve the engine for return to service. And
yes, the pilot is supposed to make an engine log entry.

I agree with you that the IA approves the engine for return to service, and
the pilot actually returns it to service. But what's your reference for
stating that the pilot is supposed to make a logbook entry? I'm not aware of
any such requirement in Part 43.