Hi Francesco, something doesn't seem right, I feel like there's more to it. I will try to help as much as I can.
I just accessed the secret menu myself, but I did not start the car, I pressed the ignition button until it was in the "ON" position. Factory manual says to start the car but not sure this is necessary for this step. I believe it has to do with other reasons. Did you access this menu with the ignition in the "ON" position?
For comparison, when I enter the secret menu and go to "Self Diagnosis", it brought up a screen similar to the one you attached in your post. Mine shows "CONTROL UNIT" in the center with "FRONT DISPLAY", "SWITCHES", "GPS ANTENNA" and "XM Antenna". Each of these blue boxes has a green line going from "CONTROL UNIT" to each of the other blue boxes (units). Each blue box will have a green square inside. That green square means the unit is operational. The lines are also green meaning it has communication with other units.
I know you don't have the "Next" button to show the next screen which tells me it doesn't know about them or is not configured to see them because if it was, then you would see the next screen with the "Sonar" and "Around View" boxes in red with red lines. Which is not the case here.
On this next screen you would see "CONTROL UNIT" with "SONAR" and "AROUND VIEW" with green lines and green squares in each blue box. Meaning they are operating normally. The green squares inside each blue box means normal operation.
There's also gray "Connection malfunction" and red "Unit malfunction". As for the lines, there's green "Normal", yellow "Connection malfunction", and red "Unit malfunction".
When I look at your vehicle, I see you have the parking sensors (sonar) and you definitely have the four cameras (around view). So these units definitely do exist in your vehicle but are not registered with the car so the car does not even try to use them.
Have you checked the fuses? I would check them and maybe replace them to be sure. From what I can see, it says fuse 34 "Battery" and 19 "Ignition switch ACC or ON". I'd still check all of them anyways.
You mentioned Infiniti programmed it...I believe they may need to do another step for the configuration to work. In the factory manual it states that if the initial programming does not work, there's an extra step they have to do.
Check to see if there's any errors recorded. If you exit the "Self Diagnosis" menu and enter the "Confirmation/Adjustment" menu, have you checked the "Error History" and does it show any errors?
You mentioned setting rear or 360 camera in menu...and then putting vehicle in reverse...are you performing this in the secret menu or through the CAMERA button? Just confirming.
Looking at the factory service manual, I see there's a few options on how to configure the new AV module. One is to save the existing configuration before replacing the AV module. Then writing the saved configuration to the car. The next option is to configure it manually which I believe that needs to be done here.
The options are as follows:
Steering -> LHD or RHD
CAMERA SYSTEM -> NONE/AVM or REAR CAMERA or REAR+SIDE
SOUND SYSTEM -> BASE or BOSE
Yours would be RHD, NONE/AVM and BOSE if I'm not mistaken.
If the write configuration is not successful the first time, the manual says to perform "Accessory Number Initialization" in the secret menu which will reboot the AV control unit. Then it says to perform the programming again.
While I was searching google, I came across this official document. Could be useful. See if the Infiniti dealer knows about this.
https://static.nhtsa.gov/odi/tsbs/2015/MC-10192613-9999.pdf