So one microcontroller with one output pin available is all you need. Since there is no clock signal, timing needs to quite tight.
To find more information you can google WS2812 or Neopixel. Libraries to use the protocol exists for most microcontrollers.
An ESP32 module is a good choice because it costs $2-3, includes wifi and BT, antenna or UF-L plug, and is pre-certified.