chore: update `basic` example to ESLint v9 and Flat Configurations. (#9501)
### Description
This PR converts our `basic` example to ESLint v9 with Flat
Configurations.
I may have a few gray hairs now, but I'm very excited for the community
to have this.
### Testing Instructions
Use `npx create-turbo@canary -e
https://github.com/vercel/turborepo/tree/shew-409f3/examples/basic
basic-eslint-9` to try it out.
- Pull it down, make sure you see diagnostics where you'd expect in your
editor. Including for `eslint-config-turbo`, most importantly!
- I know the diff is big, but there may be vestigials from my
experimenting lying around. Please use a finely toothed comb! (I've
looked myself but the more eyes, the better.)
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Co-authored-by: vincenthsh <111712068+vincenthsh@users.noreply.github.com>