Power capacitor needed with high current LED
The LED panel doesn't need a capacitor.  Your MCU does.

In fact, adding capacitance to the LED panel will make the inrush surge of the LED panel worse, not better, because the first thing that happens is that the capacitor must charge from zero to 12V.

Generally, a slight drop in the 12V rail due to an applied load will have no effect on a 5V rail regulated down from it.  You should use a proper voltage-regulator device with the appropriate power and bypass capacitors applied around it, as specified in the datasheet.

You should also use a high-frequency bypass capacitor across the MCU's power terminals, and this will also be suggested in its datasheet.  You may wish to add a more substantial power capacitor across the MCU as well, if you like the belt-and-braces approach.

When it comes to the differences between LEDs and motors, LEDs are an essentially resistive load, while motors are essentially inductive.  When a motor load is switched off it tends to generate a voltage pulse, due to attempting to pull the same current through a suddenly infinite-impedance supply.  By adding a capacitor to your motor load, you were compensating for their inherent inductiveness; you could have achieved a similar result using freewheel diodes instead.