^Most of those sound effects have been used on many different shows, and some of them predate TOS. I know the bridge sound effects were used in an episode of The Twilight Zone
years before they showed up in Trek. And the phaser sound effect is the same sound used for the levitation of the Martian war machines in War of the Worlds
, just sped up to give it a higher pitch (usually).
And Filmation had previously used those SFX in other shows like Jason of Star Command
and Flash Gordon
. Hmm, it's possible, I suppose, that Horta-Mahana licensed or bought them from Glen Glenn or Paramount or whoever for use in TAS, and thus was able to use them later in other shows.
But Trek sounds seem to be in pretty general usage now, showing up in things like Futurama
. Maybe the copyright has lapsed?