ci: add type tests for TypeScript 5.x to CI workflow

[fasttime]

Prerequisites checklist

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AI acknowledgment

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What is the purpose of this pull request?

add tests in CI

What changes did you make? (Give an overview)

This PR adds type tests for TypeScript v.5.x besides existing tests targeting TypeScript v5.3 and v6.0.

It also enables the TypeScript compiler options strict, exactOptionalPropertyTypes, verbatimModuleSyntax and erasableSyntaxOnly for all type tests, and disables type checking for JavaScript files compiled or emitted by tsc during the build.

These changes align this repo with eslint/json and eslint/markdown.

Related Issues

refs eslint/json#230

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

Question: Shall we also add type tests for TypeScript 7? It's still in the beta prerelease, but there was already a regression reported in #425 for an issue that only occurs in TypeScript 7. @eslint/eslint-team

[JoshuaKGoldberg]

Great!

Shall we also add type tests for TypeScript 7?

IMO yes, as well as TypeScript 6.

[lumirlumir]

Shall we also add type tests for TypeScript 7? It's still in the beta prerelease, but there was already a regression reported in #425 for an issue that only occurs in TypeScript 7.

I also think adding this to the CI checks would be a good idea, given adoption has grown to around 4.5M per week.

[lumirlumir]

LGTM, thanks!

Please merge this PR if you plan to add a TypeScript v7 CI check in a separate PR. Otherwise, I think including it here could also be a nice option.