Include results from `--extendedDiagnostics` when using the compiler API

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### 🔍 Search Terms

extendedDiagnostics, compiler API

### ✅ Viability Checklist

- [x] This wouldn't be a breaking change in existing TypeScript/JavaScript code
- [x] This wouldn't change the runtime behavior of existing JavaScript code
- [x] This could be implemented without emitting different JS based on the types of the expressions
- [x] This isn't a runtime feature (e.g. library functionality, non-ECMAScript syntax with JavaScript output, new syntax sugar for JS, etc.)
- [x] This isn't a request to add a new utility type: https://github.com/microsoft/TypeScript/wiki/No-New-Utility-Types
- [x] This feature would agree with the rest of our Design Goals: https://github.com/Microsoft/TypeScript/wiki/TypeScript-Design-Goals

### ⭐ Suggestion

For users of the TypeScript compiler API, it would be extremely useful to include the performance statistics obtained when using the `--extendedDiagnostics` compiler option.

From the review I've done in this codebase, it seems like this performance information is only reported when invoking `tsc` directly.

### 📃 Motivating Example

"The compiler API can now report performance information when enabling the `extendedDiagnostics` compiler option"

### 💻 Use Cases

1. What do you want to use this for? Investigating performance variations in a project that interacts with TypeScript using the compiler API.

Beginne damit nachzuverfolgen, wie die Option `--extendedDiagnostics` beim Aufruf von `tsc` Leistungsinformationen meldet, und vergleiche diesen Pfad anschließend mit der Compiler API. Lege fest, wie die Compiler API diese Statistiken bereitstellen sollte, und verifiziere, dass ein Nutzer der Compiler API sie zur Untersuchung der Performance abrufen kann.

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