"tweet on X" sounds like a gay sex thing. 

But I do think it would be helpful to have a way to sign documents with my nostr key (on mobile).

I'm a certified welding inspector. Part of my job description is certifying welders. There are currently no easy solutions to sign a PDF from my phone that don't involve paying a third party but more importantly becoming beholden to that third party to maintain the certifications that I issue.