Using linear and switching regulators in parallel for servos and microcontroller
I would run the 6V reg directly from the 11.1 volt supply too, then run the LDO from 6V instead. This would isolate the higher power servo from the others and also reduce the LDO losses.
You might even consider using a switcher to make 3.3V direct from the battery too. TI and others make triple DCDC devices that would meet your spec and reduce your chip count.
Your power sequence depends more on keeping the servos quiet until the ESP32 comes up, so you should design a reliable ‘mute’ signal to disable them.