[NorthCountryGuy]

This states there are two cooling circuits. One for engine, and one for chargers.

‘newTIS.infobeta
Home / BMW F13 M6 Coupe / Electrical Components / Connectors / Components / Components with M / M253 Coolant pump in low-temperature coolant circuit /
Coolant pump in low-temperature coolant circuit

Due to the turbocharging and the compact arrangement of the exhaust turbochargers, a large amount of heat is generated. Great importance is attributed to the cooling accordingly. In addition, an indirect charge air cooling was developed for the first time with which the charge air is cooled via an air/coolant heat exchanger. The engine cooling and charge air cooling have two separate cooling circuits. The engine control unit is also integrated in the cooling circuit for the charge air cooling.
Functional description

The electrical coolant pump works according to the principle of a centrifugal pump. The coolant pump is integrated in the cooling circuit (low temperature) and is used for the charge air cooling. Communication from the coolant pump to the engine control is effected via local interconnect network bus. The speed specification and the read-out of the current pump speed, as well as other pump values, are realised.

The following values are used for the activation:

Ambient temperature
Difference between charge air temperature and ambient temperature‘

It looks like there is one pump.
I hope the Wise chime in as I too am interested to learn more on this.