Did I break the motor, the Uno, the servo, or none of the above?

Can you warm up the whole plate and bend it around a shape ?

I'm not a fan of RGB. But there are ledstrips with four colors: Red, Green, Blue, WarmWhite. Those can give beautiful warm white pastel slowly changing colored light. If you want something fancy, then you can try those.

Adafruit RGB+WarmWhite: https://www.adafruit.com/product/2439?length=4.
Adafruit has many ledstrips and they explain how to use it. That should give an idea what can be combined with Arduino.

I hope you did not forget what I wrote about the power supply.
Suppose 5 meter ledstrip with 60 leds per meter, then you need a power supply of 5V 20A. Start with something simple.

There are also 12V ledstrips for aquariums with their own controller. Those are harder to combine with an Arduino board.