Only incompetent managers (and executives) think that "authority" is interchangeable with "respect". Fortunately for Musk, incompetence rarely disqualifies billionaires from anything.
There's no way Elon would have any respect yet, there hasn't been nearly enough time (respect is earned).
There are going to be power games for a couple of months, until the new management identifies a subset of the old staff that they can trust (or, more cynically, exploit), and then that subset will be elevated above the rest. The losers will either back down, quit, or be fired.
I'm not sure you want to use "value of his companies due to things he says" as your marker for incompetence. Many of his companies are seriously overvalued precisely because the things he says drive up the value far beyond where it should be.
Someone can be incompetent at some things and not others. We know with 100% certainty that Elon Musk is incompetent at purchasing Twitter dot com in a way that is most financially optimized for himself. We know with 100% certainty that Elon Musk is exceptionally competent at procreation.
