In my internal version of the vampire canon, vampirism is definitely a curse passed down from ancient times. When someone gets the curse, their corpse is now inhabited by the spirit of vampirism itself, which flows to fill the imprint their soul left. Like their individual curse of vampirism changes to resemble the soul it replaced. This, combined with the (internal canon) fact that vampirism can only be spread to the freshly dead, results in a brain that is mostly the same and something like a soul that is mostly like what they had before.
Think about other types of eternal (un)life, like a specter for example. In my internal canon, specters usually appear where they died and continue the action they were taking when they died. Like a specter who died in a house fire might appear in the charred husk of the house every full moon or something, just to pantomime burning to death and desperately trying to scratch through a door that won't open.
I think vampires would continue on with their mannerisms and habits that they had before, including breathing. The circuitry is still all connected for it, the muscles still work. On the flip side, the circuitry that causes panic when not breathing is also still connected. I think a vampire could easily "survive" being locked in a coffin at the bottom of the ocean... but it would be excruciating for a century or so until that neuronal connection simply burns out or fades away or whatever. Or maybe that would never happen and it would be eternal suffering.