Based on the TikTok skit I saw by @ak_iswriting. Here are my musings on how Captain Kirk from TOS could meet Captain Dr. Ryland Grace from PHM.
Both Vulcan and Erid orbit the star 40 Eridani A (Keid) and the two civilizations have known about each other even before they entered space, but due to Vulcans’ then-war-like culture and Erid’s ammonia-rich atmosphere, the two cultures rarely interacted, even after the Reformation and Vulcan’s discovery of warp speed/induction into the Federation.
When astrophage started to infect the stars, the Federation was struggling to figure out how to stop it. Meanwhile, the Eridians decided to send the ship Blip-A to Tau Ceti—as they had not yet discovered the warp drive, this process took them ~10 years (1977-1987). Due to their lack of knowledge about radiation, Rocky became the sole survivor of his crew and remained trapped in space until 2033, 12 years after Earth sent the Hail Mary.
Cannon events happen and Grace sends the Beetles back to Earth and returns with Rocky to Erid.
Due to the obvious holes in their science, the Eridians contact Vulcan with the cure. This reopens communication with the two species and Grace, leading to Starfleet being able to use the Taumeoba to cure infected stars.
Due to Grace’s already short lifespan being shortened by Erid’s 2.09 gravity (and the lack of Federation regulation), Grace is genetically modified by the Eridians, thus increasing his lifespan to resemble that of an Eridian’s (giving him ~500 additional years).
In 2063 (the year after Erid receives word that Sol has been healed), the Vulcans inform Erid and Grace that humans have achieved warp travel and first contact is being planned. Cue Grace walking Captain S’chn T’Gai Solkar through how handshakes work. It was painfully awkward for all involved.
Vulcans don’t mention to the Federation that they are in contact with the Eridians because technically that’s against the rules, given they haven’t created the warp drive yet. (It’s not like they’re helping them…officially.) Also, out of respect for Dr. Grace’s weariness of other humans, the Vulcans follow the Eridians’ lead in not mentioning Dr. Grace to humanity and the Federation at large.
Fast forward to ST: TOS (2265-69), Captain Kirk is informed that the Eridians are joining the Federation and is thrilled, as the Eridians were officially the first aliens humans came in contact with and acted as penpals with Earth since the PHM mission. Kirk remarks that it was amazing how easily Eridians communicate with humans, but isn’t surprised, given that many of them likely worked with or studied under Dr. Grace in the 21st century. Spock then drops the bomb that Dr. Grace is still alive on Erid and is going to be there to welcome Starfleet alongside Rocky and Erid’s world leaders. Kirk crashes out because Captain Dr. Ryland Grace was his hero as a kid (maybe Grace sent back videos for a few years after he left Tau Ceti to chronicle his life on Erid and the Eridians) and is promptly informed why the Vulcans haven’t made the rest of the Federation aware of his continued existence (they don’t want to piss off their Eridian neighbors by retraumatizing their already traumatized human).