Got a copy of Detective Comics, Vol. 2 #27. Going through a lot of the stories are questionable in their canonical. "Old School" is definitely not any preexisting universe. It looks like Pre-Crisis Earth-One (but can't be from that universe) but more so follows the various publishing eras of DC before ending in a meta story with Batman reading a comic in a comic shop of...well...Batman. It is said to be the 75th anniversary of Batman and this Batman is clearly that old. We must assume that in this universe Batman was created as a comics character in 1939 and that the "real" Batman must have been inspired by the comics character much later as a fan of the character. Thus, it must be its own universe.