Port ESLint plugin to Biome

Describe the feature request

I moved away from ESLint to Biome a long time ago; it would be nice to have the ESLint plugin functionality available there. (I'm not sure if Biome has a plugin architecture currently, so this might be a request for the StyleX team to contribute to the Biome source.) I think this would be structured as a Biome "domain".

I did try re-installing ESLint just for this plugin, but ESLint doesn't support TypeScript 7, which is a rabbit hole I don't want to go down.

Sibling discussion: https://github.com/biomejs/biome/discussions/11668