From what I can tell, souls get NEW BODIES when they join a Covenant. Kyrians get blue human forms. Venthyr get their vampire forms; there’s even a quest where you watch it happen.
And over in Maldraxxus, there’s dialogue where Alexandros Morgraine (I think that’s his name) and Lady Vjash why they CHOSE the forms they did. Morgraine kept his human form because that’s what he was attached to, Vash became Naga instead of Night Elf because in life, she was just a pretty face as a Night Elf, but as a Naga, did actual useful work.
So for the Kyrian and Venthyr, their appearances are basically part of their uniform. For the Maldraxi - or at least the Chosen and Eyes - they get to choose. And I THINK the Night Fae also get to choose.
Not sure why Kael’thas is running around as an elf though. From all I’ve learned, he should still be a naked soul.