Map rotation

Jeff said:

2)  I don't know why you say the map is rotating to a false North

On your video:
When you are riding - north indicator points to 11 o‘clock - means: Edge says, North ist on the left
When you stop - north indicator points to 3 o‘clock - means: Edge says: North is on the right

So, one of the 2 states must be wrong. North indicator points to a direction,  which is not North in reality - what I called „false North“.

I don't think so, if you look carefully at the map rotation, the arrow is really pointing in the same direction give or take a few degrees. Here are a couple of images off the 2nd video - the one where I wasn't following a route. There's a chunk of woods in the image so its easier to see the rotation of the map. I've also included a copy of google maps for this location - the arrow is pointing more or less north...The 1st image is from 0:38 in the video when I'm moving and north is around 10:30.  When I stop and the map flips around, the arrow is pointing at 4:00 but it is still pointing in the same direction relative to the map, just not to "my orientation." (I think of the compass as drawn on the map, you seem to be describing a floating compass that always just points north)

0:38 moving: https://photos.app.goo.gl/rjNAW7nsfeND2kHVA 

0:48 stopped https://photos.app.goo.gl/KnZFVVRrgUTCBi6MA north is still pointing more or less to that corner of the park

google map image for the area https://photos.app.goo.gl/u8Qjo95s2mCsGzDUA 

The north indicator (left top on your Edge display) behaves like a needle of a compass. It shows you where north is in real time.

First picture: you are riding, second picture: you stopped - but you did not rotate the device itself. Your device itself points to the same (track up) direction in both pictures.

Now look at the compass-needle:

You can simply check that your compass is calibrated when you go out, pick up the Edge, view the map screen, and wait for the map and your location to settle. The speed must be zero!
And now look where the north indicator is pointing and compare where north is in reality (I assume you know where north really is in your area)

Map horizontal movement

https://drive.google.com/file/d/1hPncVfftETzxL9dLjKDgcJjS8UQtAzHj/view?usp=sharing

Please check your map orientation to be „track up“ (not „north up“)
profile - navigation - map - orientation - track up

Edit:
I have to admit, that something‘s strange on your video:
It seemed to me, you have set to „north up“ but with orientation „north up“ the blue triangle of your own position should rotate and align to the street (to the left). But it seems, the triangle points upwards. And with „north up“ the north indicator should not be there.
So, it seems you have settings to „track up“ but the device acts strange...

Maybe you should reset your device...

(but in the video in your opening post - the both devices side by side - track up did work as it should. There was only a problem when you stopped)

Ok, there is a problem with your device.
If you send Garmin the short video on motorway (map moving horizontally) and setting is „track up“ then they have to admit that there is a problem!

Nevertheless - you should give it a chance. Make a hard reset of the device.