feat(typescript-estree): add type checker wrapper APIs to ParserServicesWithTypeInformation

[JoshuaKGoldberg]

Note: recreated in #6404

PR Checklist

• Addresses an existing open issue: fixes Make a "shortcut" API around TypeScript for node types #6244
• That issue was marked as accepting prs
• Steps in CONTRIBUTING.md were taken

Overview

Adds to ParserServicesWithTypeInformation the two most commonly used TypeScript type checking APIs: getSymbolAtLocation and getTypeAtLocation. Then converts all places in code that I could find that used either after immediately retrieving the TS node for an ES node.

Also applies a few standardizations that helped me find-and-replace:

• const services = util.getParserServices(context) - not a variable named parserServices, or variables from { ... }
• const checker = services.program.getTypeChecker() - not a variable named typeChecker or types, and not an intermediate program variable

Updates the Custom Rules docs page to reflect this.

[typescript-eslint]

Thanks for the PR, @JoshuaKGoldberg!

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 45 targets

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• Node 14 - nx run-many --target=build --all --parallel --exclude website --exclude website
• nx run-many --target=build --all --parallel --exclude website --exclude website

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