All of this is correct, but there is another dimension to it than that.
The truly cursed element is that the Thalmor are kind of right.
Not necessarily that the 'correct' thing to do is to genocide to return to oneness, but rather that their plan at the very least would actually work.
Because the mythology and religion of people in the Elder Scrolls world isn't a bunch of fake bullshit, it's very real in the context of their world, and magic and CHIM are constantly happening.
Meaning that mer were elements of a timeless, spaceless everything-'god'-being (Godhead?) before Lorkhan tricked the Aedra to make the world (among other things);
also I forget where men come from in the lore, I think they're also originally from the same place and were mer but got corrupted somehow, not sure though.
Thalmor are still going with the most insane and evil possible solution to something that isn't necessarily a problem though, as existing materially rather than ethereally is something they've chosen to perceive as a problem that needs solved.
And Stormcloaks is definitely the Thalmor ISIS: funded solely to sow discontent and weakness in the region regardless of who wins in the end.