Even on a simple RT-STM32F401RE-NUCLEO64 demo, modified to generate a stack overflow, the MPU feature does not trigger anything.
See the attached picture where the "compute thread" stack overflow on the blinker thread working area so the Eclipse plugin is not even capable of getting the name.

While the software stack overflow checker triggers an exception with the reason "stack overflow", as expected.
What is the expecting behavior of the MPU mechanism?
Right now, the OS seems to continue to work with erratic behavior. Most of the time, looping in the idle thread.
Edit: fix image