Different behavior of the sketch if Arduino is powered by battery

Good morning. I am creating a robot with steering controlled by a servo motor that uses the PM-R3 shield as a motor driver and is remotely controlled via a PS2 wireless controller. I noticed that when Arduino is connected via USB, loading the test sketch available at https://www.instructables.com/How-to-Interface-PS2-Wireless-Controller-W-Arduino/, my controller is recognized and both the red and green LEDs of the receiver are lit, as well as those of the controller. When, however, the same sketch is uploaded and powered through the Vin and GND pins (cables tightly secured in the PM-R3's mammoth connectors), Arduino powers on (the "ON" LEDs on both the board and the shield, as well as the red LED on the receiver, are lit), but the controller does not pair with the receiver and the green LED on the latter remains off after a brief flash of a few milliseconds upon startup, and also the "L" LED on Arduino, which is lit and steady when the board is connected via USB, does not light up in this mode.

Which Arduino?

What is voltage you used on Vin pin?

I used a 7.4V, 1200mAh RC battery. The Arduino is an UNO R3.

So you trying to use on-board voltage regulator on your UNO to power the servo? It can't work that way.
You need an external power for the servo motor.

I' m relatively new on
Arduino, but I know a project that uses, like as me, that battery to power on Arduino using the Vin line and controls the servo with the digital pin 3. https://www.instructables.com/Servo-Motor-Car-With-Arduino/.
P.S: I' m attempting to realize the same project with the same hardware and starting from the same code.