feat(utils): add types for both flat and legacy eslint classes

[bradzacher]

PR Checklist

• Addresses an existing open issue: ESLint v9 Support #8211
• That issue was marked as accepting prs
• Steps in Contributing were taken

Overview

• Add types for the new FlatESlint class.
• Rename and export types for the LegacyESLint class.
• Deprecate the existing ESLint class.
• Add missing types from the docs.

[typescript-eslint]

Thanks for the PR, @bradzacher!

typescript-eslint is a 100% community driven project, and we are incredibly grateful that you are contributing to that community.

The core maintainers work on this in their personal time, so please understand that it may not be possible for them to review your work immediately.

Thanks again!

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✅ Successfully ran 31 targets

• nx test eslint-plugin
• nx test eslint-plugin --coverage=false
• nx test typescript-eslint
• nx test visitor-keys
• nx test utils
• nx run types:build
• nx test type-utils
• nx test rule-schema-to-typescript-types
• nx run repo-tools:postinstall-script
• nx test typescript-estree
• nx test scope-manager
• nx test eslint-plugin-internal
• nx test parser
• nx test repo-tools
• nx run-many --target=lint --parallel --exclude eslint-plugin
• nx test ast-spec
• nx run-many --target=build --parallel --exclude=website --exclude=website-eslint
• nx run-many --target=typecheck --parallel
• nx test visitor-keys --coverage=false
• nx test eslint-plugin-internal --coverage=false
• nx test typescript-eslint --coverage=false
• nx test type-utils --coverage=false
• nx test scope-manager --coverage=false
• nx test parser --coverage=false
• nx test rule-schema-to-typescript-types --coverage=false
• nx test typescript-estree --coverage=false
• nx test utils --coverage=false
• nx test repo-tools --coverage=false
• nx run integration-tests:test
• nx test ast-spec --coverage=false
• nx run repo-tools:generate-configs

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