Not having a go at you, but, out of curiosity, given your question about how common the acting style of Trek was, how much American genre television from the sixties have you been exposed to? How much is available to you on streaming platforms and the like?
Over here, post the digital transition, we've had an explosion of over-the-air digital networks specifically dedicated to airing reruns of vintage programming. They have largely taken the programmining role that used to be held for decades by small, local, non-network affiliated stations for decades before the ascendancy of cable.
So, for many of us, we grew up practically marinated in vintage mid-to-late sixties reruns: Star Trek, Batman, Lost in Space, The Wild, Wild West, the Man from UNCLE, Mission: Impossible, Dragnet, Adam-12, the color Gunsmoke episodes, Bonanza, the Big Valley, etc.
If any of those are available to you, and you're curious to see how Star Trek's acting and production styles stack up in comparison, I'd recommend checking out a few episodes from those series.