Great Googly Moogly It's All Gone To Shit

The events of PHM start in the late 2010s or early 2020s and have Grace and Rocky getting to 40 Eridani in the late 2030s. Vulcan's first contact with Earth takes place in Star Trek canon in April 2063, and by that point they had been quietly monitoring Earth for some time. They definitely knew a LOT about humans by the 2030s - physiology and disease conditions, human languages, Terran technology, probably a general grasp of Earth geopolitics and cultures too. They would have known about the Petrova line in our system and may have even known about PHM to some extent.

Generally speaking, though, Vulcans are arrogant dicks about pre-warp cultures in a "white man's burden" kind of way, and they do not interfere with pre-warp civilizations, even technologically advanced ones facing a world-ending crisis. They wouldn't have gotten involved with Stratt et al. or tried to help us in any way, even though Earth and Vulcan were dealing with the exact same crisis. They would detect us launching the Hail Mary, make note of it, and set some kind of unmanned probe or attach a device to the hull to track it and see where it's headed.

However, I don't think any Vulcans monitoring Earth would believe we'd have even a slight chance of pulling off a manned interstellar mission with the resources we had available, even with cutting edge Earth tech powered by astrophage fuel. Hell, they might have even tracked Grace all the way to Tau Ceti but assumed the ship and remaining crew was lost during the fishing trip, like if their sensors were destroyed or detached when Grace was trying to pull the ship out of the atmosphere.

As for Erid, Vulcan may not have even noticed the Eridians. They're pre-spaceflight right up until they launch Blip-A, don't use light- or radio-based communication, are silicon-based and subterranean, and live on a planet completely inhospitable for carbon-based life. As far as the Vulcans know, Erid is a barren planet in their home system with an intensely hot, high-pressure ammonia-based atmosphere that can't support any form of life as they know it.

For that matter, even Blip-A could have gone mostly unnoticed when it was launched. Eridian tech is made out of xenonite, an exotic material they either a) have never seen or thought possible, as with Grace, or b) have possibly seen before but don't know how to synthesize or use. Rocky's ship would most likely appear on their scanners as a big pocket of xenon gas surrounding some chunks of rocky material and a quantity of astrophage, which exits a barren planet's atmosphere and then leaves their system. They'd for sure want to study it and would likely send an exploratory mission to investigate and track it - to them, it looks like a barren planet in their system just ejected a plume of astrophage, planetary atmosphere, xenon gas, and rocky debris, so logically they're going to follow up on it.

Once they get a visual on it and see it's a construction clearly made by some kind of sentient life, though, non-interference principles kick in. Their scanners won't pick up any life signs or breathable atmosphere on board, so it will look like it's an unmanned probe propelling itself somewhere. This, of course, would be its own mystery for the Vulcans and they will still keep tracking and studying it. Nonetheless, it still wouldn't point to there being life on board or native life on Erid, since the Vulcans otherwise wouldn't learn about silicon-based life until the crew of the USS Enterprise discovers it in the 23rd Century, and thus wouldn't think to look for it.

With all that said, I'm imagining the Vulcans' absolute shock when their sensors pick up something entering their system, only to discover it's that same primitive Earth spaceship they started tracking almost 20 years earlier, the one they thought was lost at Tau Ceti. It's battered all to hell but still working - not only that, it's got A HUMAN LIFE SIGN ON BOARD. It can't be hailed so they tractor it in, and inside they find one human scientist, alive and mostly lucid but also very unwell, who goes bug-eyed when he sees them. He goes to speak but can't get his words past his astonished stammering. He shakily holds out an odd-looking Earth device, and finally manages to get out,

"Grace. *points at self*

Friend Rocky. *points to the enclosure behind him*

Taumeba. *points to a door across the room*

Translator."

He hands them the device and flashes a delirious, wide-eyed grin before hitting them with the LLAP 🖖🏼 and collapsing. After the Vulcans rush Grace to medical and get him examined, stabilized, nourished, and rested, they are able to debrief them via Grace and Rocky's homebrew English-Eridian translator and the English-Vulcan translator they've developed during their years surveying Earth.

The Vulcan Science Academy is buzzing with excitement (in their subdued Vulcan way) once the findings are published, and they all find themselves marveling at the extremely improbable story of Dr. Ryland Grace, Earth scientist, who:

survived 18 continuous years in space against all odds with no other humans on board (including extended time in an unsupervised medically-induced coma, and multiple dangerous spacewalks) on a ship they believed to have likely been destroyed years ago.

never trained for space flight before he was shanghaied into space and then lost his pilot and engineer before he even woke up

successfully collected biological samples from another planet in a risky upper-atmosphere maneuver that nearly killed him, and then used them to develop a cure for the astrophage that's also killing Vulcan's star (in a small lab on his ship and with only the resources he had available).

had no means of rapid communication with Earth, zero chance of rescue if anything went wrong, and had initially understood he was going to die in space whether or not his mission was a success.

was the first human in Earth's history to make first contact with a sentient alien species of any kind.

learns to communicate with said alien, and, when they discover their common goal, immediately starts working together as a team to complete their mission, forming a profoundly deep friendship in the process.

might have actually made it back to Earth after all, had he not sacrificed his chance at going home by going back to rescue the alien friend he made and make sure he gets home with his batch of the astrophage cure, saving both Sol and 40 Eridani.

And his friend 🎶🎵Rocky 🎶🎵:

Who comes from a neighboring planet in Vulcan's system that they always thought to be completely uninhabitable and devoid of life

Who belongs to a technologically advanced race of silicon-based lifeforms, which they had never seen before and thought was theoretical at best

Whose species learned to synthesize a previously-unknown metallic alloy of a noble gas into an extremely versatile building material and can spin filaments of this material into objects manually like a Terran spider spinning a web.

Whose species has no innate or learned concept of relativity, no concept of light and radiation and no sense of sight, and navigates using a highly developed form of echolocation...

...and, despite all of that, achieved interstellar travel, in a ship so alien to the Vulcans that they first mistook it for a giant pocket of gas and then tracked it for years believing it was unmanned and constructed by another space-faring civilization.

like Grace, was the first member of HIS species to make first contact with a sentient alien species and immediately befriends him.

Engineered an entire system so he and his new friend could work and live together despite their drastically different atmospheric needs.

Risked his life by leaving his atmosphere bubble to save his friend's life at Tau Ceti, severely injuring himself in the process.

Gives Grace some of his fuel to get back to Earth because he loves him and cannot bear the thought of him dying in space, knowing that doing so will add another six years until he finally gets home to his people and his mate.

Grace still takes all the time he wants to decide what he's going to do with the rest of his life. Vulcan, having warp technology and faster-than-light travel, develops a plan to seek out and inoculate affected stars with Taumeba. The science academy acknowledges that they owe their existence to members of two species who successfully traveled to distant stars without FTL travel, leading them to rethink their approach to encounters with pre-warp civilizations.

Grace has a standing invite to study, research, and teach at the science academy. Sometimes he does, and he'll be the first to admit that it's still a trip to know that Vulcans exist and they actually do the 🖖🏼 thing in real life.

Ultimately though, Erid, along with Rocky and Adrian and all their pebbles, becomes his real home.