5v boost module shutdown with servo

I can't imagine the (unloaded) servo pulling 800mA.

According to this page. the MG90S stall current is 680 +/-50 mA, so plan on 800 mA (with a safety margin). It will draw that every time it starts up.

As I pointed out earlier, the starting current drawn from the battery could be around twice that.

Take heart, you are not alone! At least 95% of the servo problems reported almost daily on this forum are due to inadequate power supplies.