The only thing that Cohen has done is shut down stores and cut costs massively at the expensive of revenue. He hasn't really fixed anything, he is just managing their demise. All of his strategic initiatives like expansion of e-commerce or an NFT platform were complete disasters that had to be wound down. The only reason the company is even showing a profit is because they repeatedly diluted shareholders to raise cash and then re-invested that money into Treasuries. Basically, if you are buying GME stock, you are getting an expensive fixed income wrapper.

Buying EBAY would be a bad deal for pretty much everyone involved. GME shareholders get diluted to buy EBAY for way too much money. EBAY shareholders get paid in vastly overvalued GME shares. And the entire thing would be managed by some guy whose only strategic idea is to cut costs. The only one who would benefit is Cohen, because it would create a sufficiently liquid market for him to sell his stake, something that is not currently possible in GME.