The reason Bosmer are the ones that most prominently mention this in their myths is because their ability to shape their surrounding plantlife has direct ties to the pact they made with Yffre. The other races don't talk about it as much because after Yffre became the earth bones, they became ordered and that was that. They had no need to make a pact with him to shape their surroundings.

I don't buy that at all, I'm afraid. The Bosmeri myths do not say that they made the pact with Y'ffre in order to gain power over nature. They specifically say that they couldn't keep a constant shape without Y'ffre's pact, and the same goes for the Khajiit and Azura. They also consistently place themselves and not other races as the beneficiaries of this intervention. It's not just a matter of other mythologies not mentioning it, it's also that the Bosmeri and Khajiit mythologies claim it was only them.

For example, in Words of Clan Mother Ahnissi:

But Nirni soon forgave Lorkhaj for Nirni could make children. And she filled herself with children, but cried because her favorite children, the forest people, did not know their shape.

And Azurah came to her and said, "Poor Nirni, stop your tears. Azurah makes for you a gift of a new people." Nirni stopped weeping, and Azurah spoke the First Secret to the Moons and they parted and let Azurah pass. And Azurah took some forest people who were torn between man and beast, and she placed them in the best deserts and forests on Nirni. And Azurah in her wisdom made them of many shapes, one for every purpose. And Azurah named them Khajiit and told them her Second Secret and taught them the value of secrets. And Azurah bound the new Khajiit to the Lunar Lattice, as is proper for Nirni's secret defenders. Then Azurah spoke the Third Secret, and the Moons shone down on the marshes and their light became sugar.

But Y'ffer heard the First Secret and snuck in behind Azurah. And Y'ffer could not appreciate secrets, and he told Nirni of Azurah's trick. So Nirni made the deserts hot and the sands biting. And Nirni made the forests wet and filled with poisons. And Nirni thanked Y'ffer and let him change the forest people also. And Y'ffer did not have Azurah's subtle wisdom, so Y'ffer made the forest people Elves always and never beasts. And Y'ffer named them Bosmer. And from that moment they were no longer in the same litter as the Khajiit.

Here we have Ahnissi specifying forest people who became Bosmer or Khajiit. Nobody else.

Likewise, The Ooze speaks only of wood elves, of Bosmer, as being subject to the Pact (and thus able to have a Wild Hunt). The Bosmer have this ability because they were of the forest people that Ahnissi mentions, not because they started out in a Dragon Break. If it applied to anyone who was in a Dragon Break, then it would apply to non-elves, too, like humans! And I'm fairly sure it doesn't. Varieties of Faith does claim that they believe "the first mortals" were shifting, but I'm much more inclined to trust the actual Bosmer and Khajiit tales than an Imperial scholar's interpretations.

Additionally, all of these events happened after linear time had already begun, during the Merethic. Nothing happens on Tamriel until after Convention, so the forest people that became Bosmer and Khajiit weren't subject to the non-linearity of the Dawn. They had trouble keeping their shapes for entirely different reasons, which is made evident when you consider that Y'ffre's Pact and the Lunar Lattice apparently do not protect them or their lands during other Dragon Breaks (if Dragon Breaks even do carry with them shape changes for everything; I'd need to see more convincing texts than I've yet seen to believe that). And also consider that they're descended from Aldmer, who hadn't yet suffered their schisms until well into the Merethic.

Re: All mer having this ability: "Mer" is also just a word that means person/people. That statement doesn't mean that all elves have the ability; notice that he said the Bosmer were going to call it. I think reading that as saying any elf can take part in a Wild Hunt is a bit of a stretch, especially considering that would be the only source to ever mention it, if so. And plus, the Wild Hunt is specifically the result of going back on the Pact with Y'ffre (the Pact isn't just about being able to tell stories about nature, it's very much related to the Wild Hunt specifically). If the other races didn't make the Pact in the first place, how can they go back on it?

Re: Stuhn and Tsun and Trinimac: The Aedric aspects are a totally different thing, and Nord storytelling isn't the most trustworthy.

So, yeah, all in all I do not find this case very convincing. From what I see, the forest people couldn't keep their forms during the Merethic Era, and two gods helped them become two peoples. The other races had their own things going on.

Yes, but you wouldn't say something like "a car, also known as the engine" or "a human being, also known as the brain" or something like that. It very clearly refers to Ada-Mantia also being known as the Zero Stone.

And yet, in the very same document, it also says that Stones are different from Towers, that every Tower has a Stone, and that their "forebears saw the erection of Ada-mantia, Ur-Tower, and the Zero Stone." Like I said, Nu-Hatta is playing fast and loose with the nomenclature after establishing that Towers and Stones work together to produce their effects, and are distinct objects.

Ada-Mantia, Ur-Tower, and Zero Stone could simply be different aspects of the same structure.

It's entirely possible that Adamantia is being used as a name for the conjunction of Ur-Tower/Direnni Tower and the Zero Stone; that is, together they form the mythitectural structure known as Adamantia. But I still very much doubt that the Zero Stone is one and the same as Ur-Tower. Nu-Hatta is quite clear that they are different objects, and so is Once. If the Zero Stone were a wall they'd call it a wall.

At this point, though, I feel like we're just going in circles.