The last phase of MoveRangeCoordinator, which is responsible for releasing the critical section, scheduling range deletion, and related tasks, currently has two separate execution paths that perform essentially the same work.

The first path is taken during the coordinator's initial execution, when _migrationAttempt is not null. The second path is taken on subsequent executions.

The goal of this ticket is to unify these two paths into a single flow in order to simplify the code.