Bill has always been very conscious of his legacy and perception. Brady winning doesn't help him, but it doesn't hurt him that much, as long as he also does well. If he doesn't do well for a long period of time though, he may retire with serious doubts about being the GOAT coach. If this season doesn't go the way Bill wants it to, and he doesn't have a good core set up for next year or hit on a young QB, I could see him bowing out to save face. It isn't like he's young either.
Not only that, if this year goes badly for Bill then things become MUCH tougher for him. He has already lost a fair amount of credibility with the players and FA after what happened this year, if he loses next year too then he will lose any allure he had to make this place a destination. Without that all he will have is a team with problems at QB, a grump hard ass coach no one wants to play with, and no one buying it to take less.
One players stop buying in you're done. No coach or manager is immune to that no matter how good you are. At some point a fresh start and reset becomes more valuable then the better coach, as odd as that sounds. So here is a hot take. If Bill loses again next year, the team is better off moving on from him. As hard as that is to swallow. It doesn't mean he isn't the best coach of all time automatically, it is just the reality of locker room culture and how quickly it can shift. It's a big reason Bill made all those excuses last year. He needs to convince his team it was just a speed bump. If they stop believe that then all is lost.