Sauron is a recently recovered Maiar. Gandalf is a Maiar recently incorporated.
I'm loving the "As an angelic being, I don't know how to operate as in an approximation of a mortal body. I don't even know how mortal-like minds work" approach.
Imagine downloading a human being into an ant's body: there isn't enough brain to store our thoughts. Sure, you can cheat (give it "enhancements" - in SF, you'd imagine a tiny supercomputer to boost its brain power), but it is an ant, the form factor puts serious limits on how much cheating you can do.
So the Wizards don't fit in their (mortal-ish) bodies.
I also wonder how much of the "I don't really fit in a mortal body" impacts Sauron. There is the injuries and defeat and his recovery from them as another explanation, plus the fact he's sort of hiding.