There are a few key differences. PE tries not to massively overpay, it'll put more effort into targeted layoffs, and it'll maintain enough of a "business as usual" posture to not scare away advertisers. Edit: they also put in a CEO whose full-time job is being CEO of that company.
But yes, this is very bad execution of the PE playbook.
Elon thinks he's brilliant at everything he tries his hand at, so he thought he'd jump into the private-equity arena and show everyone how brilliant he is.
But yes, this is very bad execution of the PE playbook.