SWA start is broken when using Vite and TypeScript

Before filing this issue, please ensure you're using the latest CLI by running `swa --version` and comparing to the latest version on [npm](https://www.npmjs.com/package/@azure/static-web-apps-cli).

swa version: 2.0.6

**Are you accessing the CLI from the default port `:4280` ?**

- [ ] No, I am using a different port number (`--port`) and accessing the CLI from that port
- [x] Yes, I am accessing the CLI from port `:4280`

> Make sure you are accessing the URL printed in the console when running `swa start`!

**ℹ️ NOTE: Make sure to enable debug logs when running any `swa` commands using `--verbose=silly`**

**Describe the bug**
When using latest Vite (>=6.3.5) dev server and a TypeScript project, SWA CLI fails to load through the dev proxy (:4280) while it work using the Vite dev server directly (:5173).


The issue seems to that the MIME type is changed when going through the SWA proxy, changing from `text/javascript` to `video/m2pt`.

**To Reproduce**
Steps to reproduce the behavior:

1. Create a new project folder, and run `npm create vite@latest repro -- --template lit-ts`
2. `cd repro && npm install && npm install -D @azure/static-web-apps-cli`
3. Add this `swa-cli.config.json`:
```json
{
"$schema": "https://aka.ms/azure/static-web-apps-cli/schema",
"configurations": {
"registration-website": {
"appLocation": ".",
"run": "npm run dev",
"appDevServerUrl": "http://localhost:5173"
}
}
}

```
4. Run `npx swa start`

**Expected behavior**
Requests going through the proxy do not alter the MIME type

**Desktop (please complete the following information):**

- OS: MacOS
- Version 15.4.1 (24E263)