I didn't hear the exact statements by Shams but it certainly sounds like he is signed for 3 more years at $14M, guaranteed. I am not all that worried about the contract and I suspect the Celtics aren't either. I don't think this will prevent them from making a coaching change.
To me, it is about whether Mazzulla can get the team to buy in. There was reporting of owners and players shouting at each other and that the players "never got over" the firing of Udoka. It is hard for the new coach to get buy in if the players are still wishing they had their old coach. To me, this is the critical issue.
The players need to get over Udoka, he is not coming back. But it may be easier for them to get over this if they have a more established coach, or maybe it won't. It is going to be really tough on the team if every time there is a rough stretch, the players start thinking, Udoka was a better coach, why did they fire him.
In the end, I have some doubts about Mazzulla as a coach. Not so much over Xs and Os (although I have some doubts with that) but more over buy in. It may be no fault of his but the Udoka shadow may make it impossible for Mazzulla to succeed.
As to the schemes, I don't think the team's offensive schemes are sophisticated enough. There needs to be more action off the ball. More player movement off the ball. More cutting, more off ball screens. I acknowledge that it can take more than 1 season for that level of offensive scheme to start working but I just did not see it. Not with this team and also not with Udoka either.