the term you want to research is "steganography"
I think in the case of pico8 it actually just has a tiny slice of binary data represented as RGB pixels at the bottom maybe? or I may be wrong
If I remember correctly, spore stores all the fun details in its .pngs by encoding it in some form via the alpha channel which you can see if you open one up and mess with the transparency
or you can sort of see it in mangled form here via the time I uploaded a guy to Twitter and tweetdeck ate the transparency leaving the data sprinkles visible for all to see
like apparently you can put arbitrary metadata into a png file but maxis did it this way instead
You can export blueprints of entire little Lego cars of shocking complexity and just swap them around. You always know exactly which blueprint you're dealing with because boom bam it's just a picture!
you don't even need to do anything particularly clever or secret to accomplish this
PNG is a chunk based format (yes this sounds ridiculous to say but each building block is actually formally called a chunk) so things like your header (IHDR), palette (PLTE, if any), image data (IDAT), and so on
So if you wanted to, you could basically just make up your own private chunk type and stuff whatever information you wanted in there. The specification supports this! You're given explicit permission to just make up whatever as long as you do it in a way that won't break officially supported chunks!
But yeah pico-8 does it the steganography way. Probably one, because pico-8 is a fun little toy and that's a fun way to do it. And two, image data will survive reencoding on the web (etc) as long as it's lossless, while most reencoders probably won't know what to do with your private chunk data and would just discard it.