Starting with Windows 11 25H2 Build 26200.7019 (or 26100.7019 on 24H2) and newer, “Update and shut down" will shut down, not reboot.
So, when you click "Update and shut down" on your PC, you assume your PC will install any available updates, then shut down.
The bug is breaking the “X” button to quit Task Manager, preventing the app from shutting down and instead keeping it running ...