No, they don't specify that they're undead in any of them. None of them even test it or note the change from life to death to life again. They assume that since they "looked" dead that they must have been.
Yes, they do specify vampires as undead (all those three books). You are right, none of them test it, but as I explained previously - there are hundreds of vampires and it is very unlikely that no one ever tried to test it. Those reports aren't present in the game (because it just can't contain everything) but the texts I mentioned are there. Why would scholars who wrote them believe that vampires are undead when there would be a proof to suggest otherwise? Well, because there is no proof that they are alive, because they are undead. Why would Mannimarco (The God of Worms, the king of necromancers) believe that vampires are undead if it wasn't true?
That is quite a bizarre attack on a straw man. No one claimed nobles can't be turned into vampires. The very text you failed to use as evidence for your views states that "few victims survive vampiric attacks or feedings."
Few out of thousands or maybe tens of thousands is still quite a lot.
You only find it logical to assume because it supports your position. (most likely, the distinguishing Ash vampires is done to separate them from blood vampires, who among other things, are commonly believed to be incurable) Turn undead not working on vamps in game is evidence that they are not effected by magic meant to effect the undead. And you have nothing to contradict that.
I wonder if turn undead works on those ghosts in KotN (since they are NPC)? I tried to google if vampires are really not affected by turn undead in game, I couldn't find anything. Although some vampires are part of the faction called "undead" in game.