Bug: esbuild builder 3rd party libs built not properly with browserify paths

### Command

serve

### Is this a regression?

- [ ] Yes, this behavior used to work in the previous version

### The previous version in which this bug was not present was

none

### Description

We're currently in the evaluation of replacing the Webpack with ESBuild process from Angular.

The only blocker right now is, that the path replacements for the building process does not work as expected and the application directly crashes into a white screen.

### Minimal Reproduction

https://github.com/JohnnyDevNull/angular17-esbuild-browserify-error

1. Checkout the mentioned reproduction repo
2. `npm install`
3. `ng serve`

Open the app and you will directly see an Vite warning and the error from the 3rd party library we are using `fhir` in this case for the healthcare sector.

```
Module "stream" has been externalized for browser compatibility. Cannot access "stream.Stream" in client code. See https://vitejs.dev/guide/troubleshooting.html#module-externalized-for-browser-compatibility for more details.
```


```
Uncaught TypeError: Cannot read properties of undefined (reading 'prototype')
```



As you can see in the configs below I've added the `paths` and `browser` properties to help esbuild understand the mapping, but it does not work anyways.

Just to mention, the 3rd party library is a CommonJS library, which we cannot avoid here, so its added to the `allowedCommonJsDependencies` configuration.

tsconfig.json
```
/* To learn more about this file see: https://angular.io/config/tsconfig. */
{
"compileOnSave": false,
"compilerOptions": {
"outDir": "./dist/out-tsc",
"strict": true,
"noImplicitOverride": true,
"noPropertyAccessFromIndexSignature": true,
"noImplicitReturns": true,
"noFallthroughCasesInSwitch": true,
"skipLibCheck": true,
"esModuleInterop": true,
"sourceMap": true,
"declaration": false,
"experimentalDecorators": true,
"moduleResolution": "node",
"importHelpers": true,
"target": "ES2022",
"module": "ES2022",
"useDefineForClassFields": false,
"lib": [
"ES2022",
"dom"
],
"baseUrl": ".",
"paths": {
"stream": ["node_modules/stream-browserify"]
}
},
"angularCompilerOptions": {
"enableI18nLegacyMessageIdFormat": false,
"strictInjectionParameters": true,
"strictInputAccessModifiers": true,
"strictTemplates": true
}
}
```

package.json
```
{
"name": "ng-dummy",
"version": "0.0.0",
"scripts": {
"ng": "ng",
"start": "ng serve",
"build": "ng build",
"watch": "ng build --watch --configuration development",
"test": "ng test"
},
"private": true,
"dependencies": {
"@angular/animations": "^17.3.0",
"@angular/common": "^17.3.0",
"@angular/compiler": "^17.3.0",
"@angular/core": "^17.3.0",
"@angular/forms": "^17.3.0",
"@angular/platform-browser": "^17.3.0",
"@angular/platform-browser-dynamic": "^17.3.0",
"@angular/router": "^17.3.0",
"fhir": "^4.12.0",
"rxjs": "~7.8.0",
"stream-browserify": "^3.0.0",
"tslib": "^2.3.0",
"zone.js": "~0.14.3"
},
"devDependencies": {
"@angular-devkit/build-angular": "^17.3.4",
"@angular/cli": "^17.3.4",
"@angular/compiler-cli": "^17.3.0",
"@types/fhir": "^0.0.41",
"@types/jasmine": "~5.1.0",
"jasmine-core": "~5.1.0",
"karma": "~6.4.0",
"karma-chrome-launcher": "~3.2.0",
"karma-coverage": "~2.2.0",
"karma-jasmine": "~5.1.0",
"karma-jasmine-html-reporter": "~2.1.0",
"typescript": "~5.4.2"
},
"browser": {
"stream": "stream-browserify"
}
}
```

### Exception or Error

```
Module "stream" has been externalized for browser compatibility. Cannot access "stream.Stream" in client code. See https://vitejs.dev/guide/troubleshooting.html#module-externalized-for-browser-compatibility for more details.
```

```
Uncaught TypeError: Cannot read properties of undefined (reading 'prototype')
```

### Your Environment

```text
_ _ ____ _ ___
/ \ _ __ __ _ _ _| | __ _ _ __ / ___| | |_ _|
/ △ \ | '_ \ / _` | | | | |/ _` | '__| | | | | | |
/ ___ \| | | | (_| | |_| | | (_| | | | |___| |___ | |
/_/ \_\_| |_|\__, |\__,_|_|\__,_|_| \____|_____|___|
|___/

Angular CLI: 17.3.4
Node: 18.19.1
Package Manager: npm 10.2.4
OS: darwin arm64

Angular: 17.3.4
... animations, cli, common, compiler, compiler-cli, core, forms
... platform-browser, platform-browser-dynamic, router

Package Version
---------------------------------------------------------
@angular-devkit/architect 0.1703.4
@angular-devkit/build-angular 17.3.4
@angular-devkit/core 17.3.4
@angular-devkit/schematics 17.3.4
@schematics/angular 17.3.4
rxjs 7.8.1
typescript 5.4.5
zone.js 0.14.4
```

### Anything else relevant?

This issue was already reported with https://github.com/angular/angular-cli/issues/26901 but sadly to say closed. I hope you have now a better picture with my simple reproduction repo.

Klone das verlinkte Reproduktions-Repository, führe npm install und ng serve aus und bestätige die Vite-Warnung zur Externalisierung sowie den Laufzeitfehler. Untersuche, wie der esbuild-Builder das Pfad-Mapping in tsconfig.json und das Browser-Mapping in package.json behandelt; abgeschlossen ist die Aufgabe, wenn die fhir-Abhängigkeit ohne die stream-Warnung oder den Prototype-Fehler geladen wird.

Vom Indexierungsmodell aus dem Issue-Text verfasst.