At the time, there were dedicated companies that provided sound effects for many different shows, using their own standard libraries of effects. Filmation's sound effects and music editing were usually provided by the Horta-Mahana Corporation, although they weren't credited on TAS. TOS's sound effects were provided by Glen Glenn Sound. But I think there was some overlap between the sound effects libraries.
Must have been. Seemingly every sound effect used in TOS was on He-Man: photon torpedoes, transporter beam, red alert klaxon, even, I think, TOS bridge sounds. Until recently when my kids got the e-Man DVDs, I didn't realize just how many effects were reused.