If it is just a trademark issue and not logo design, could Twitter just make it x.com? Elon made x.com in 1999. He could pitch it as a revival rather than simple X the company.
I don't know how that works though. What if it just dies on the grapevine and no one uses it for 2 decades? AFAIK It got merged into Paypal then was mostly just killed off as a functional trademark
Meta, Microsoft Apple and Google have all used X for one thing or another. Most recently an X trademark in the context of social media was bought by Meta from Microsoft when they acquired Mixer, which became Facebook Gaming.