So, I do not want to be presumptive, or to wade into waters over my head, but my CFI told me that the "legal" requirement (in 2024, for single engine general aviation aircraft that are not rented or used commercially) is that a "record" be kept that an IA signed the aircraft off as being airworthy and that all of the relevant ADs had been complied with within the past 12 months. No "log", let alone separate aircraft, engine, and propeller logs are "legally" required. (Not that they are not useful, and quite valuable, just that they not "legally" required.) That if one wanted to, one could "record" the inspection in catsup on an old pizza box, and discard everything save the AD list upon completion of the next annual inspection.