Actually, the lawsuit claims they do have evidence. Some of the evidence they claim to have is in the form of video tapes and texts -- though it is unclear what type of evidence they have about the attempted selling of pardons. It will be interesting as the evidence is revealed, and how strong it is.
I did find it interesting
what Barr said about the idea that Rudy may have been selling pardons, and splitting the money with Pres. Trump. Barr things very carefully about it for several seconds, then states, “Uh, I’m skeptical about that. I don’t think Rudy Giuliani would do that. I hope he wouldn’t, but I don’t know.” Barr, who knows both Giuliani and Trump, didn't sound nearly as certain about it as you do. Also interesting that he states he doesn't believe Rudy would do it but doesn't say the same about Trump. I also found it interesting that it took Giuliani almost two full days to issue a denial, and even then he did it by putting out a statement through his publicist.
I believe 1) most AG's would come out strongly and say there is no way the President they worked for would have sold pardons, that it was completely unbelievable, and 2) that most people would have immediately come out with a denial about selling pardons. It will be interesting to see what evidence is uncovered as the trial progresses.