LEDs are put in a matrix, similar to a keyboard matrix, with only one portion of the matrix activated at once. That takes care of the power consumption. By flickering faster than the eye can notice, it looks steady. The brightness of a LED is controlled by how much relative time it is lit vs. dark.
Dedicated RGB LED controller chips are usually used to get fine-grained control of colour of each RGB LED, and so that the main microcontroller can do other things.
I would looking at the ISSI IS31FL3733 chip. You'd need two of them for 120 keys though, but that should work (Input Club K-Type/Massdrop Ctrl uses two for both backlight and sideglow). There is support for it (and others) in QMK.