He got an auto raise with the Cup. He wanted astronomically more, so sure that contributed, but I believe the decision to move on from Barry was made well before the Cup win.
I don’t think it ever got to the point where someone like Leonsis pushed back on what Barry ended up signing for.
No decision made in advance would have been so set in stone that it could not have been un done if the Caps won a Cup. In fact the Caps did win the Cup, it triggered a raise and more term for BT, and GMBM publicly stated that if BT wants to be here, he will be here. And then BT quit. So BT did NOT want to be here.
We still don't, and never will, know what went on in those negotiations, or if there ever were any meaningful negotiations with BT .and BM. But that's not most important. BT quit while under contract, so what BM wanted isn't important anymore. BT wanted out.