Shifting Connected Over and Over and Over....

Yes.  I have seen this

I have the same with my Fuel EXE and XO Transmission1040 to the point I have turned off the beeps on my 1040.  It still records the data and shows it in the Sram AXS app though. My regular MTB with GX AXS does not have the connection bug.  Not sure if the T-type has a weaker signal or if there is some EM interference with the bike's electronics or maybe a combination of both.

One of these days maybe I will unplug and put a battery on the derailleur and try it with the bike powered down to see if it makes a difference.

The part I don't understand and think it has to do with the E-Bike is the message says "shifting Connected" I don't have any of my sensors named "shifting" 

I'm pretty sure "Shifting" is the name of the sensor category that AXS is located in.  Are you sure you don't have your AXS connected? Since the transmission builds include the main battery connection to the derailleur, it's on when the bike is on so it would be easy to add it and not notice it.

On the Sensors list it will have a symbol that looks like a chain ring sprocket.  If you tap on it, it will say Shifting at the top of the screen, and if you tap on Sensor Details you can adjust the front and rear cog sizes.

I reached out to SRAM tech-support and they sent me this information. Might be helpful.

This is with the power being sourced from the bike, not the AXS battery.

When a TQ motor starts applying torque, the Ant+ signal from the RD will drop, leading to the behaviour that you've noticed. Interestingly, this does not occur when a standard AXS battery is installed. From some testing we've done on our end, the issue doesn't occur when an AXS battery is installed in place of the Extension Cord, so the rear derailleur's Ant+ channel is being interrupted/blocked by interference transmitted by the TQ motor (when it is applying torque). If interference is being piped to the rear derailleur through the extension cord, the only solution to receive uninterrupted shift data may be to use an AXS battery. 

I have the same problem on a Scott with a TQ motor, I was also suspecting it was the motor, it happens particularly when I'm climbing and more power is required. What disturbs me though is that I haven't had this problem for the first months I've owned the bike, so it seems it has been introduced at a certain point, maybe a firmware update?

Do you also have XO? This did not happen when I had GX.

No just AXS

Please let us know if you find a solution