Well, for starters, Ymir is def dead. There's no point proving that she's alive.
Now, The Coordinate/The Paths. Now, before we start explaining, there's some things we have to set clear. First, the "parasite that gave Ymir her powers is def some kind of god , it does act like a parasite, lacking onto someone and never letting go,"protecting" them (in some cases, if you get what i mean), and reproduces by their host being eaten, climbing into another host. But it doesn't make sense how it creates demonic-like beings and making daydreams come alive, so my only guess is that it's a parasite.
Alr, now, the Coordinate. The thing that would make most sense is that the Coordinate is a place where users of the titans go after they die/ get eaten, as you can see in the new episode that new branches grew from the Coordinate when Ymir's body was eaten, and excactly 3. Maybe when a titan user dies , they rest forever in their branch, with ymir being the tree, something like in Death Note, where the Death Note users later become Shinigamis. If you use this theory, then the answer is that Ymir is dead, and her status in the Coordinate heaven is to create titans and do... idk, dead people stuff?
Also, I think that the Coordinate works the same ways for Eldians, since they can all be summoned there , and there are A LOT of branches in the Coordinate... It makes no sense, and i have no idea how it works, but this is my mere theory of it