If I'm reading that HAL code correctly, the PWM callback function is getting called early in the process. You may just be exceeding the performance boundaries of the chip.

• Make sure you don't have some other interrupt active at the same time that's blocking your timer interrupt from excecuting.
• If you need some bit of hardware (like an ADC) synchronized to the PWM pulse, then you may want to do that in hardware, with a separate timing output.
• If you can stand some uncertainty about whether your code will pop off slightly before or after the PWM pulse, and you have the timer resources, you can have a separate timer that goes off some predictable time before your PWM output goes off. This will require either an unused capture/compare channel on the timer you're using, or the ability to put another timer into service and synchronize it to your "master" timer.

The code above was correct. The break points were "temporary hardware" breakpoints, when I changed them to "hardware" breakpoints they where hit when there was a counter overflow indicating that the period was reached.

Typical case of staring at the same code for far too long ;-)

You should add the type of htim in the function declaration which is missing in:

void HAL_TIM_PeriodElapsedCallback(&htim3)
{
  HAL_GPIO_TogglePin(N_CS_GPIO_Port, N_CS_Pin);
}

By adding it you will get:

void HAL_TIM_PeriodElapsedCallback(TIM_HandleTypeDef *htim)
{
  HAL_GPIO_TogglePin(N_CS_GPIO_Port, N_CS_Pin);
}

To check if the function is called for timer 3, check for the correct timer:

void HAL_TIM_PeriodElapsedCallback(TIM_HandleTypeDef *htim)
{
   if (htim == &htim3)
   {
      HAL_GPIO_TogglePin(N_CS_GPIO_Port, N_CS_Pin);
   }
}

(I do not have a compiler at hand, so I cannot check the code).

I had a similar situations and after a bit of digging traced it down to this statement in the ST drivers IRQ Handler, the same that you have included in the question:

if(__HAL_TIM_GET_IT_SOURCE(htim, TIM_IT_UPDATE) !=RESET)

Confusingly named, this line is actually checking whether the Update callback is enabled.

I therefore was able to trigger the callback once I enabled the TIM_IT_UPDATE feature...

This can be done in two ways (links are referencing the G4 HAL drivers):

Using the HAL_TIM_Base_Start_IT() (Not Recommended)

Which enables this feature as a consequence

HAL_TIM_Base_Start_IT(htim)

Note: This is only "not recommended" as you are using the OC mode

Using __HAL_TIM_ENABLE_IT()

Running this in an initializing section (e.g. HAL_TIM_OC_MspInit()) :

__HAL_TIM_ENABLE_IT(htim, TIM_IT_UPDATE);

Notes

I would probably suggest the second option if it works for you, as the ST docstring suggests the former is for setting the timer as a Timer base, which may have unintended consequences for this use case.