Technically speaking it just needs to be in the “Aircraft records”…whatever those might be. The official sign-off has to be somewhere, and the most logical place is the airframe log, because that goes with the airframe no matter how many different engines or props it has in its lifetime.
I make an entry in the engine and prop logs with the work done during the inspection, and usually say “as part of the aircraft condition inspection”….but this isn’t required.
Paul