build: use typescript-eslint@v6 with reworked configs

[JoshuaKGoldberg]

Internal Tooling

(Please pardon my hijacking the feature template - this was the closest I could find. ❤️)

Coming over from typescript-eslint/typescript-eslint#6760: typescript-eslint is soon going to release a new v6 major version with reworked configurations. You can read up on it here: typescript-eslint.io/blog/announcing-typescript-eslint-v6-beta

Specifically, the configurations are reworked so that the preset rule configs we recommend for most projects are:

• 'plugin:@typescript-eslint/recommended-type-checked'
• 'plugin:@typescript-eslint/stylistic-type-checked'

I'll send a draft PR showing what the changes would look like here. Is this something you'd be interested in? 🙂

(sibling issue on redux-toolkit: reduxjs/redux-toolkit#3540)