systick timer configuration in microsecond for stm32c031c6 MCU

You mean, running the SysTick *interrupt* at a MHz rate? It's a bad idea.

Instead, you can run a timer with prescaler set so that is counter increments at a MHz rate, you can treat that counter (i.e. TIMx_CNT) as the SysTick counting variable (taking into mind that the timer may be 16-bit).

JW

At 1 MHz the only thing the MCU would do is enter/exit the SysTick_Handler continously.

Find another method to achieve whatever you're trying to do.

A TIM clocking at 1 MHz, or higher, can count off time in micro-seconds or better.