I haven't seen the TOS episodes in a long time and had forgotten some details. That a Starfleet officer would choose to live in isolation on Talos-IV forever rather than return to the world because she has scars on her face didn't seem nearly as weird the last time. It really sticks out when set against the rest of Disco, though.

Vina wasn't a Starfleets; her ship was a survey ship contracted by some organization called the American Continent Institute. Although that's at least partly because there's no mention of Starfleet at all until 'The Menagerie', which was the 15th episode in production order. Prior to that it had various different names throughout season one of TOS, including Space Central, Galactic, and the United Earth Space Probe Agency.