eeprom is just memory. it’s basically just memory holding the contents of the game. the actual processing occurs on the console. as far as netbsd on atari… i doubt it. and even if you could you’d have a hard time arguing what you got running was actually netbsd.
if i was going about it… i’d create a controller for a MUCH LARGER memory pool and have that interact with the atari… bootstrap into netbsd and run off the hacked memory cartridge controller device.
Arguable if that would be considered legit. But it’d be a hilarious project.
It would take days to boot even a severely stripped down kernel, especially with the insane level of bank switching you would need. I also have some doubts that you could get a text console working on an Atari 2600. It’s almost impossible to overstate how incredibly primitive the Atari 2600 hardware is. Getting Space Invaders to work on the 2600 was almost a miracle. Pac Man was too much for the console (the version that came out was horribly stripped down). The hardware was specced to play Pong. Two paddles, one ball, and not much else. It’s really amazing what people were able to do with it.
128 bytes of working memory (which would include the stack, kernel variables, and everything) is just absurdly tight, and your ROM has to be bank switched in 4k chunks.
I’ve seen projects that struggle mightily but get a webserver running on a Commodore 64. A C=64 has 512 times as much memory as an Atari 2600.