Recently I've discovered this design for a 0.4" x 0.4" arduino compatible board:
https://hackaday.io/project/3117-a-even-smaller-nanite FNF

My proposal:

• a similarily sized Tinyduino, possibly powered by a small battery cell
• a neopixel addon board which can be soldered to the bottom side of the board (using spacers)

This is a really cool idea! A Tinyduino that small could open up tons of possibilities for ultra-compact projects. The idea of adding a neopixel board is awesome too, though, like you mentioned, power management will be key—neopixels can drain a battery fast, especially in compact setups. If you could implement some sort of low-power mode or dynamic brightness control, that could really help extend battery life. Excited to see how this could evolve!

I have set up a few 13 inch CRT  televisions as novelty or decor melon sandbox items for my friends. I outfit them with an analog TV converter box with a USB media player. They play old video footage on USB.

The Tiny TV style player would be so much better for these things. Loading up a bank of retro "cable" channels, Startup and go with no menu diving (the menus the analog converters have are difficult to view on small CRT's anyway) and having the channel flipping action like the Tiny TV has would be awesome & nostalgic. My old analog converters work like a media player rather than a retro cable box.

I totally get where you're coming from! The whole Tiny TV style setup would definitely be a game changer for these CRT setups—nostalgic channel flipping is such a great touch. The analog converters, while functional, really aren't the best for small screens, and the menus can be a pain to navigate. Having a smoother, more intuitive experience like the Tiny TV would make everything feel more authentic and enjoyable. Plus, the idea of just powering it on and having those 'retro channels' already set up is the kind of convenience I think a lot of people would appreciate