Hello,
We also deployed two Windows Server 2025 nodes and installed Exchange SE in a DAG. There is currently a bug in the Failover Cluster service of Windows Server 2025 where the core resources will not failover when the system stops or reboot. There are also an issue with the quorum. You may find some critical events and errors in your Event Viewer (FailoverClustering event id 1561 and FailoverClustering-Client event id 81 in our case). At least it will tell you if your issue come from this.
After opening a support case on this, a KIR registry key was applied. It solved the problem for a few days and it now back. It seems to happen again since 2025-10 Cumulative Update.
Not solved yet...