Only incompetent managers (and executives) think that "authority" is interchangeable with "respect". Fortunately for Musk, incompetence rarely disqualifies billionaires from anything.
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.
Source: Seen a couple management changes before.
In my experience, outside tech bro circles he is unanimously regarded as an idiot and not someone to emulate.