I had a phone that did that, out of lazyness or malice, it would turn on completely (load the full android OS) any time it had any cpu wakeup from the poweroff state instead of its OEM screens made for that purpose (like the battery charging while at 0%, "need more charge to power on" screen). This includes but not limited to:
if the device charging state has changed (powers on rather than show the "charging" screen).
hardware alarms including the disabled sceduled power on or off.
pressing hardware buttons (like the volume rocker or power button)
Sounds like the phone's battery is weak and so whenever the phone needs a lot of power immediately from the battery it fails to give enough power to the device. That's what it sounds like from here. You can probably read more if you look into Apple battery gate and how they were slowing older iPhones