Hello Thank you for the information.
It was useful for me as well.

Please allow me to add:

How to find out the Vendor ID and Product ID
It is briefly displayed along the info message on the bottom left hand side of the screen:
Tetris Opening Screen showing Error message and the values for the controller presenting the issue

With lsusb we can see in Hexa the values
Bus 001 Device 014: ID 045e:0b12 Microsoft Corp. Xbox Wireless Controller (model 1914)
Changing the controller does not change the ID.
However, changing the controller for a generic controller changes the ID:
Bus 001 Device 016: ID 045e:028e Microsoft Corp. Xbox360 Controller
Hence causing this to happen AGAIN, which is annoying.
We have to manually edit the config file again.

One thing that bothered me is that in all know previous versions of Retropie this was not an issue and now it's presenting one new, more issue than the previous version.
I've used Retropie for years now and I have never had this issue.
The only "new things" I have are

Operating System [Ubuntu 22.04 LTS freshly installed]; THIS Specific controller (Tested and proven to be working in all other games, also the old controller presented the same issue); USB Cable (Tested and proven to be working on other games, and able to "quickly charge" a Phone and perform fast data transfers)

Please let me ask:

Is there any way I can make it Automatic when I change controller to change the configuration.
-- Bear In mind I did the controller configuration at the start of Retropie every time I change the controller, and I tested quite a handful of times, I went as far as deleting , removing configuration files, and recompiling Retropie from the source 3 or 4 times. Would there be any test you'd like me to perform?
-- I may test it again on another Ubuntu version (or Ubuntu based distribution);
-- I don't discard the possibility to install it on a different Linux Distribution;

Thank you very Much.

@amplifuzz did you try and remap or check the mapping in the Retroarch menu?

Pull up the menu depending on your controller but SNES style controllers is select+X. Then Quick Menu - controls - input section. See if you can remap it there or change the mapping to fit your controller.

Also...remember C64 games also have joystick port settings to switch. But sound like uiu already have that covered.