Do you think the shiite nations will just sit quietly in the background while this evolves?

No. That is the other risk factor - and opportunity.

Their capabilities have been sharply degraded by Israel, which is part of why Hamas was in a position where they had to take this deal. It will be years before the Shiite countries can have the capacity to project influence into Gaza the way they did before. Having lost those lines of resources, Hamas was seriously weakened. But they will still try to make sure that Gaza stays unstable, and certainly can cause some amount of problems.

But the opportunity is that the Sunni nations will see this as a limited window to block Shia influence in Gaza. Letting Gaza become a failed state would leave it open for greater Shi'a influence if, as and when those nations begin to rebuild their capabilities.

We don't even yet know, though, whether the other ME states want to take control of Gaza in any meaningful way. If Hamas is determined to stay in power, they've got 10K-20K soldiers - and they've already started killing their political opponents and anyone who they think might be a potential threat in a post-war world. We'll see.