Twitter already has a lot of debt, far too much to fund this.

Twitter has no equity. There's nothing to leverage.

Unless I'm missing something, 'leveraged buyout' doesn't specify that it's Twitter's equity which has to be leveraged. Off the top of my head, I think Elon Musk has some other bits and pieces which he could scrounge together for collateral.

No, leveraged buyout means you use the equity of the company purchased as the backing for the loan.

If you borrow from somewhere else it’s just a buyout.

Hm, that doesn’t sound right, and Wikipedia agrees with my understanding, that an LBO means the buyer borrows money for it:

>> A leveraged buyout (LBO) is one company's acquisition of another company using a significant amount of borrowed money (leverage) to meet the cost of acquisition. The assets of the company being acquired are often used as collateral for the loans, along with the assets of the acquiring company.

Note how the second sentence says that the assets of the purchased company can be part of the arrangement, but the “L” in LBO means the buyer’s borrowing, however they accomplish that.

https://en.wikipedia.org/wiki/Leveraged_buyout