Here is a minimal setup demonstrating how to write a new ESLint. You'll notice a rule in src/rules/if-newline.ts. This rule is exported from src/index.ts and the REPL is automatically stubbing your src directory out to the dist directory which is why you can see ./dist/index.mjs is able to be imported into your eslint.config.js file.
You will also find a test here, which you can run in the terminal with npm test. Make changes and watch your tests update accordingly as is expected with Vitest.
Initial example from https://github.com/antfu/eslint-plugin-antfu - look at that repo for more tips.
Other sources for info on writing rules: