FWIW my ebike and the SRAM AXS system do not communicate or share power supply. The derailleur has its little rechargeable battery and the shifters are each powered by a common button cell.

AXS will communicate with a bike computer and my Garmin shows charge status for all three components. Helpfully, it also shows selected gear, giving tooth counts and ratio. (If you're mental, you can see how many shifts per ride in Connect.) Separately, the shifters and derailleur have a little blinky code warning of low battery state. One must look to see it of course.

The derailleur battery needs charging roughly monthly and the shifter batteries last two years. Guess if the derailleur battery were to go flat one would be in the chosen gear the rest of the ride. Unlike a broken shift cable that sends the derailleur to the smallest cog. Is one better? IDK. Can one keep a spare cable/spare battery in their kit? That's a big 10-4. Changing a battery is quicker than stringing and adjusting a cable.