Angle sensor to count the rotational periods

Is there a sensor or mode to count in both directions the rotational periods of the motor like a multi turn encoder?

Yes, the MA780 has this feature and the parameter MULTI(2:0) features to count up to 8 bit = 256 periods of full rotation. And counting as incrementing or decrementing this period counter depending on the rotation direction. With the SPI interface this data is available. Mind that the sensors update rate needs to be < 180deg angular change to be able counting the periodic revolutions.
For more see https://www.monolithicpower.com/en/catalog/product/view/id/3769/s/ma780/category/114/