@paco Awesome, thank you; I will read those over carefully
This is what I had been looking at: https://www.aliexpress.us/item/3256807311563265.html
Also alibaba, I just needed some validation that I was operating in the right ballpark and wasn't missing something obvious. I'd gravitated to these because they are RGBW.
@david I ordered
These light strings
This power supply (I got 10A, which is overkill, but my 4 strands easily pull 4A)
This ESP8266
Someone gave me the ESP8266, so I don't have the exact source/spec, but that looks like it. There are a few versions of the NODEMCU 8266, and that one's small. What I like about it is that 5V, Ground, and D4 are right next to each other on the D1 mini, so I can make a nice little 3-pin connector for it.