EXTI stops working after jumping to the new firmware STM32L4
You are starting the other application from within the interrupt serice routine, never returning from the interrupt handler. The system won't execute the same interrupt handler (or any other handler with the same or lower priority) until a proper exception return sequence is executed. You should somehow exit all active handlers before jumping to the other firmware.

Simplest method is to set a global volatile flag in the interrupt handler, and check it periodically in your main applocation loop.

You can also reset the system using NVIC_SystemReset(). You'd need a way to check and communicate where did the reset request come from, as it always goes to the first application.

Also note that __disable_irq; does nothing, you'd need () to actually call a function. It's always a good idea to enable and check compiler warnings.