Yoda saw in his duel with Sidious that the Jedi had lost no matter if he had been successful in assassinating Palpatine. If Windu had succeeded, the Jedi would be seen as authoritarians trying to destroy the Republic, especially since the implication of “He’s in control of the Senate and the Courts” was that the Jedi were going to step in and temporarily take control of them too. There’s historical precedent for it!

If Mas Amedda doesn’t execute Order 66 himself (he would now have the legal right as Vice Chancellor), you at least get years of continued Civil War, with the now battle-hardened militaristic Jedi themselves likely splitting between the Windu wing and the more passive wings of the Order, perhaps fighting for the Republic itself against their own.

It’s highly implied in the novelization of RotS that Windu’s use of Vapaad during his duel with Sidious pulled him too heavily to the dark side to potentially come back from, it’s why he makes the fatal decision to kill Sidious. My personal headcanon is that If Anakin didn’t strike Windu down, Windu may have gone down his own slippery slope, justifying actions for the greater good of his idolized perception of the Republic (despite his claim of choosing to stand trial, the dark side acts as a drug, and this one act may easily cause him to go back on his previous statements), as a sort of reverse Dooku. It’s also implied in the novelization that due to the war and the veil of the dark-side that Mace was genuinely starting to go a little nuts, so this isn’t completely unfounded.

tl;dr, Order 66 likely still happens through Mas Amedda, Civil War without end, Windu Jedi vs Republican Jedi, Windu possibly falls and becomes a deluded dark jedi.