Typecheck code blocks in jsdoc

### 🔍 Search Terms

jsdoc typecheck

### ✅ 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

When a codeblock is created in jsdoc, apply typechecking on it as if it were part of the code in the file.

### 📃 Motivating Example

I create a method that has a non-trivial function signature (example is contrived)
```ts
type OtherType = { data: TData };
class Class {
doSomething(arg: OtherType): void;
}
```
I would like to document the idiomatic usage in jsdoc
```ts
/**
* Does something, example:
* ```ts
* const cls = new Class<{ x: number }>();
* cls.doSomething({ data: { x: 1, y: 2 } });
* ```
*/
```
If the function signature or underlying types change in any way, the typechecker will tell me to update the usages, but not the example.
The example becomes outdated potentially unknowingly, potentially causing bad code that could have been prevented if the example was typechecked.

### 💻 Use Cases

1. What do you want to use this for?

Typecheck code blocks in jsdoc

2. What shortcomings exist with current approaches?

Relying on implementations as the idiomatic way when the example in the jsdoc is intended the be the idiomatic way.

3. What workarounds are you using in the meantime?

Inspection

No files, tests, or entry points are named. Research should identify the JSDoc code-block and type-checking entry points, then define tests showing that examples are checked against surrounding declarations without changing emitted JavaScript.

Written by the indexing model from the issue text.