feat!: Rename FlatESLint to ESLint

[nzakas]

Prerequisites checklist

• I have read the contributing guidelines.

What is the purpose of this pull request? (put an "X" next to an item)

[ ] Documentation update
[ ] Bug fix (template)
[ ] New rule (template)
[ ] Changes an existing rule (template)
[ ] Add autofix to a rule
[ ] Add a CLI option
[x] Add something to the core
[ ] Other, please explain:

What changes did you make? (Give an overview)

1. Renamed ESLint to LegacyESLint
2. Renamed FlatESLint to ESLint
3. Updated the related tests
4. Updated the related docs
5. Updated the migration guide

Is there anything you'd like reviewers to focus on?

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[mdjermanovic]

LGTM, thanks!

I found a few more things that should be updated in docs, tests, and comments, but since this PR could easily run into merge conflicts, I'm going to merge it now and prepare a follow-up PR.