Of the top of my head an Arduino mega might do it (54 GPIO pins) plenty of ram and plenty fast for such a simple task. My only reservation there would be total current. LEDs tend to be on the high side but doable for driving direct from a GPIO but you need to balance that against overloading banks of GPIOs that have their own limits.

Otherwise you could look at simple shift registers with a smaller MCU such as 74HC595 to give you extra pins with less current limitations. Or look at LED driver ICs that give you PWM capability such as MAX6974 and similar

And lastly there are addressable LEDs these days that give you a lot of capability in a very small package such as WS2812 and similar.

Any of the non direct GPIO options can be implemented with pretty small/basic MCUs like the various arduinos and compatibles.