Display files with errors summary in `--watch` mode

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### 🔍 Search Terms

file listing watch mode
file summary watch mode

### ✅ 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 running `tsc` with the `--watch` flag, we should see a list of files with errors, similar to what you see when running without `--watch`.

**Running without watch**

```
npx tsc
src/bar.ts:3:5 - error TS2554: Expected 0 arguments, but got 1.

3 bar(1);
~

src/foo.ts:2:3 - error TS18048: 'a' is possibly 'undefined'.

2 a.toString();
~

👇
Found 2 errors in 2 files.

Errors Files
1 src/bar.ts:3 👈 these are clickable and I don't have to scroll up the terminal to see them
1 src/foo.ts:2

👆
```

**Running with watch mode**

First run:
```
[9:49:05 AM] Starting compilation in watch mode...

src/bar.ts:3:5 - error TS2554: Expected 0 arguments, but got 1.

3 bar(1);
~

src/foo.ts:2:3 - error TS18048: 'a' is possibly 'undefined'.

2 a.toString();
~

[9:49:05 AM] Found 2 errors. Watching for file changes.
```

After a file change to bar.ts

```[9:49:53 AM] File change detected. Starting incremental compilation...

src/bar.ts:5:5 - error TS2554: Expected 0 arguments, but got 1.

5 bar(2);
~

src/foo.ts:2:3 - error TS18048: 'a' is possibly 'undefined'.

2 a.toString();
~

[9:49:53 AM] Found 2 errors. Watching for file changes.

```

**The ask**

Either by default, or with an option (`--showFileSummaryInWatchMode` ?) show the file summary when running with watch mode.

### 📃 Motivating Example

When running the TypeScript compiler in watch mode, you now have the option to see the list of files with errors.

### 💻 Use Cases

The main use case I have in mind, is for when I make a breaking change to a type in my codebase, and I need to know the impact this change can have.

Because these file paths are clickable in most IDEs (On MacOS cmd+click will open the file in the IDE), this file list can be a very convenient starting point to see the impact/make changes.

eg. I make a change to type X making a property optional, and I can see that this causes type errors in files A, B, C. I got to file A and to fix the type error, I make a return property there optional. I now see additional errors in files H,I,J,K,L,M,N,O. I abandon this approach.

### Related

https://github.com/Microsoft/TypeScript/issues/22124 - This is about pretty mode and watch mode. It's essentially asking the same thing 'I don't need to see all the details of the errors, I just want to see the file count'.

The issue is marked as completed - but I can't see that it actually does what the OP wants. AFAICT all it does is add colors to the terminal.

Commencez au point d’entrée de tsc --watch et comparez sa sortie de diagnostics avec celle d’une exécution normale de tsc. Reproduisez les exemples de l’issue, puis déterminez si le résumé des fichiers doit être le comportement par défaut ou une option. Le travail est terminé lorsque le mode watch affiche, après chaque compilation, un résumé cliquable des fichiers contenant des erreurs.

Rédigé par le modèle d'indexation à partir du texte de l'issue.