I can't hear the noise in the video, but if it sounds like a power hand drill then the starter is spinning but the solenoid did not push the Bendix out into the flywheel/flexplate, check ignition or stuck relay / short in starter wiring. If it sounds like a clicking noise it could be the solenoid trying to push the Bendix out, or the relays chattering if it is coming from the relay box. Check for same as above.
Because you have been having trouble keeping it charged, I would remove the ignition start wire from the starter and check for voltage between it and ground while hooked to a fresh battery or high power wall car charger. If no voltage, go through the motions of starting with key and recheck. If there is voltage with the key out/off then it is most likely an ignition issue/short. If NO voltage is found have the starter checked. A sticky solenoid/non-disengaging ignition/short can cause this issue, but this is generally harder to do, so generally, I would check this last unless the first test shows voltage.