This mostly correctly describes a leveraged buyout (LBO). LBOs are done by LBO shops, a type of private equity (PE) firm. Not VCs. (VCS do venture capital, a different type of PE.) And LBO debt isn’t “pushed” onto the company’s books, it’s never on the sponsor’s (LBO shop’s) books in the first place to any material extent.
Private credit, on the other hand, involves e.g. Blue Owl borrowing from a bank to lend to software businesses, usually without any taking control or equity. It’s fundamentally different from both LBOs and VC or any private equity inasmuch as it doesn’t have anything to do with the equity, just the debt. (Though some private credit firms will turn around and lend into a merger or LBO. And I’m sure some of them get equity kickers. But in that capacity they’re competing with banks. Not PE. Certainly not VC, though growth capital muddles the line between what is VC and other kinds of PE or even project financing.)