Back power liftgate not working properly

From the description and the video it looks like the rear lift gearing has failed. To get access to it you need to remove the left side D-Pillar trim panel, that is the one all the way at the rear between the floor and ceiling. To remove it you remove the trim strips across the top and the bottom of the rear hatch, then remove the seat belt loop on short wheelbase and the bolt holding the seat belt on the long wheelbase vans. Then the panel pulls free of the clips. Disconnect the speaker if needed.
With that out of the way you will see the motor assembly on the pillar. Remove the wiring and then unbolt the lift assembly and lift it up and out. Now you can inspect the gearing and the levers to see where the failure is.
The motor number is 5019036AA and looks like the below image. The plastic piece is a common failure as it the internal gear.
Replacement of the motor is done by unbolting the motor from the lift assembly and bolting on the replacement. Then you install it and use a scan tool to erase any fault codes from the liftgate module.

The motor is supposed to pull a short cable that releases the secondary latch and then starts lifting the hatch up. Then once it comes back down the latch closes and the motor in the latch pulls the hatch down fully to the locked position. With the motor not assisting that second latch doesn't move enough to release it. The key bypasses the lift motor and the secondary latch so it will open.

Okay, the lack of the gas struts likely overstressed the motor. It's really nothing more than a seat motor with different linkage. The beeping should sound and then the motor lifts the gate. It also looks like the gearing needs a bit of lube. The drive gear should move away from the drive pinion when you lift the gate manually, that is part of the emergency system so you can yank the interior handle to open the hatch even without power. Yours might be the later version that repurposed the release cable to the hold open latch. They changed them a couple times when they had problems with the gates staying up. With the new struts and getting the motor to work, should take care of it, oh and add some white lithium spray into the latch and those drive gears.

It's supposed to if it's on, but only the manual release is supposed to be disabled. The remote and other buttons should still work. It's a mechanical system and should only prevent the interior release handle from working. It moves a piece inside the latch that keeps the handle from working.

The motor has to come off the lift and should have 3 bolts holding it to the lift assembly. It has been a while so I don't recall if the wiring connection is out in the open on that one. If it is you could unplug it and check to see if you have battery voltage at the tan wire with orange and the tan wire with brown wires when you hit the open close button. If you have that but no motor motion it's a bad motor. If you don't have that then it could be the door control module which could fail but it's usually the motor.
Because of the way it works a good scan tool can also talk to that module but it needs to be one that has full coverage and bi-directional control. I've only seen one failed module and it did nothing when you tried anything with the gate, even the latch was shut off.