This is a classic problem for people who didn't grow up making 8-bit pixel art. Typing "pixel art" into Nano-Banana only creates the illusion of pixel art, which quickly breaks down under modest scrutiny, particularly at larger resolutions.
That's why you can see "smeared edges," "fringing," etc.
Even a basic nearest neighbor downscale/upscale would have squashed some of the higher frequency noise.
OP: Look into palette reduction and pixel grids. This is a decent start as a post-processing tool for this stuff.
https://github.com/jenissimo/unfake.js