Add support for ESLint v9

[gund]

Add support for ESLint v9 while maintaining backwards compatibility with all previously supported ESLint versions.

Closes #78

This PR is cannot be finished until:

• [x] Library is migrated to ESLint v9 in BC way
  • [x] Migrate context.getAncestors() API usages
  • [x] #86
• [ ] Library is passing all tests
• [x] BC test is added to make sure v8 still works
• [x] Upstream dependencies add support for ESLint v9
  • [x] typescript-eslint

[piotr-cz]

It looks like typescript-eslint is supporting flat configs now:

• https://typescript-eslint.io/getting-started#step-2-configuration
• https://github.com/typescript-eslint/typescript-eslint/issues/8211#issuecomment-1949436642

[Noumanluckey8057]

https://github.com/typescript-eslint/typescript-eslint/issues/8211#issue-2069340518

[JoshuaKGoldberg]

👋 @gund are you still planning on working on this soon?

[JoshuaKGoldberg]

As in: I'm happy to hop in and write a PR, but don't want to step on your toes. 🙂

[liquidg3]

@JoshuaKGoldberg - thought I was commenting on this earlier 😂 - hoping you can hop in and get this over the line if @gund is tied up! Thanks to you both for the hard work!