I've seen this episode a number of times, most recently in late 2022. It's definitely an example of William Shatner's versatility as an actor. Throughout the run of the classic series his acting was terrific, just what the situation demanded. It was during the movie era when he had become a caricature of himself on the way to pop culture popularity.
Compared to the sequel series starting with Star Trek: The Next Generation right through the streaming series of today, Star Trek is virtually Shakespearean in its sparse use of stage sets and its character interactions.
Regarding Spock's treatment of Yeoman Rand when she reported her encounter with Other Captain Kirk, we have to keep in mind that it was only Episode 4 of Season 1. Spock's character was still being crafted or finalized. It was later in the series we discover that he is half-Vulcan and half-Human, and that made it possible to write nuanced Spock stories going forward. At the time of S01E04, though, we just knew him merely as an alien who was cold toward his shipmates, even if he had empathy toward them.