... How are syscalls dealt in other RTOS using MPU?
For the case of the MPU, there is no general answer to that. I don't think that there is any standard model for the use of the MPU in a Unix-like system.
NuttX uses the MPU to create a Kernel space with the OS and critical board logic in it and a separate user space for applications. That is inspired by the standard Unix kernel + applications model.
But every use of the MPU that I am familiar with in deeply embedded bare-metal or tiny RTOS systems are totally custom solutions.
For the MMU (which you might think of as an MPU with address mapping), the Unix model is the only one I am familiar with. As in Linux, a kernel blob and applications loaded into RAM from a file system.
Greg