Yes. See [1] for an overview of how this works.

When the SEC filing is made, we'll get to see how the deal is structured. The $20 billion from TD Securities becomes a debt obligation of the combined company. There's a tax break in equity to debt conversion, and a second tax break for carried interest. [2] There may be a preferred stock deal or debt refinancing so that TD gets their $20 billion back. Usually, the private equity firm exits within a few years.

[1] https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.23.1.121

[2] https://www.pgpf.org/article/what-is-the-carried-interest-lo...

That's just for the cash part. The stock part makes no sense. For this 50/50 deal to work in principle, they'd need to issue around a billion new shares, which would massively dilute the existing ~450M shares. So Ebay shareholders would suddenly own 70% of Gamestop after the deal. It's also highly questionable if investors actually believe the combined stock is worth that much, so the stock price would probably fall and turn those 70% into >90%. At this point it basically becomes a reverse acquisition plus a large loan for the final company from the cash part of the deal.

No, unless any control transaction using any leverage counts.

A third of the deal is financed with debt. A fifth is financed with cash. The bulk—fifty percent—is being financed with equity. An LBO would see debt and a thin tranche of cash finance the bulk of the acquisition.

The stock part is more like a merger than a buyout.

Yup.