By definition a hostile takeover is one that is done without the blessing/recommendation of the current board of directors.

Most private takeovers are negotiated by the board/management (ostensibly on behalf of the shareholders). Going over their head and straight to shareholders is when it's called a hostile takeover.

As far as Elon not planning to replace the board/management. I would say that it is a foregone conclusion that he will clean house if his takeover succeeds. He has been actively critical of their management.