This was an all-cash buyout. It does not mean it was not leveraged.
All-cash buyouts are those buyouts where the acquirer pays with cash and not their own stock. In this case, Musk used only cash.
But some of that cash (about $12.7 BN) was borrowed from banks. So, it was leveraged.
In principle some buyer like Musk could buy without any help from banks, but why would they do that? You don't get to be a multi-billionaire without getting familiar with financing.
In any case, leveraged or not, Musk did not saddle Twitter with any debt. Maybe he will do it in the future, but for the time being he didn't, because he did not have time to do it.
He could try to issue a huge amount of debt later, and pay himself an extremely fat dividend, so he can turn a quick profit. But in the current market environment, that does not seem even remotely likely. Who is going to buy newly issued Twitter bonds? At what yields? A one year US Treasury yields 4.8%, what type of yield would one require for a bond issued by Twitter? 10%? 15%? If investors get a hint that Musk is just trying to run Twitter into the ground and get himself a nice exit, they won't invest even at 30%. After the whole saga with Musk repeatedly changing his mind on the deal (and before that the $420-for-sure Tesla buyout), how many investors do you think would fall for a get-rich-quick scheme perpetrated by a guy who can't actually climb the richest man ladder anymore?