To my understanding, this at the moment is neither hostile nor a takeover, but a (rather direct/rude/aggressive; pick whatever adjective you want) question to the board to advise shareholders to accept Musk’s offer.

It could become any of the four options failed takeover, failed hostile takeover, takeover, or hostile takeover.

If the board says “good idea” and advises shareholders to accept the offer, it could or could not become a takeover, depending on whether enough shareholders (by share count) accept it (I don’t know how many is enough, but it’s almost certainly more than 50%, as an OK would force _all_ shareholders to sell. You can’t take a company private and keep shareholders around)

Technically, that wouldn’t be a hostile takeover, though, as it would be with agreement by the board.

If the board advises shareholders to reject the offer Musk could persevere. In the end, if enough shareholders sell their shares to him, the board’s opinion doesn’t matter. if enough shareholders do that, it would become a hostile takeover.