Sensor supplied by MCU - sink or source what is most energy efficient?
For the safety of the device, you cannot use the "sink" disconnecting the ground could lead to unreliable operation. Further, disconnecting the ground will also not prevent the 100nF capacitor from discharging. The OH49E will still load the capacitor and discharge it when the MCU tri-states the CTRL port. Efficiency is only a matter of on time versus off time for the sensor device.

An additional problem is that the OH49E does not have a turn-on specification. It appears to be intended only for constant-supply operation. You will have to determine by testing how long it takes for the output to stabilize for an accurate reading. The suggestion by Chris Stratton in the comment about using interrupts and a reed switch would likely be more efficient because only the low-power MCU would be drawing power. The pull-up resistor for the switch could also be large to have only a small current when the door is opened.