Repo: Enable ESLint's eqeqeq internally

### Suggestion

This comes up once in a while. I was surprised to see it's not enabled in any ruleset already.

https://eslint.org/docs/latest/rules/eqeqeq

> ```js
> ["error", "always", {"null": "ignore"}]
> ```

Example of where this has come up: https://github.com/typescript-eslint/typescript-eslint/pull/6091#discussion_r1050381489