B737 MAX 9 Captain reported the aircraft went into standby power mode; started depleting the battery; and would not switch to a different electrical source while taxiing to the gate.

Narrative

After landing and waiting the three-minute cool down period; we shut down engine number two. Approaching the gate; we started the APU. When the APU blue available light illuminated; I asked the First Officer (FO) to bring the APU generator online. The FO attempted to put the APU on the right bus. When they selected the switch; the aircraft went into standby power mode and started depleting the battery. The aircraft wouldn't allow any more switching of electrical sources. The number one generator light was not illuminated; and should still have been providing power; but apparently was not. We got operations on COM one and told them we would need a GPU hooked up immediately. When the GPU was plugged in the aircraft would not accept its power until I shut down the number one engine and the APU. I wrote up the aircraft; conversed with station maintenance; and also followed up with a conversation with Maintenance Control. This was a very strange occurrence and needs to be looked into and fixed. This could have been a big deal inflight. If the engine two generator would have failed and the APU turned on to cover the bus this aircraft may have went into standby power mode. I'm glad this happened on the ground taxiing in.