Add Rush as a package manager

### Is there an existing issue for this?

- [x] I have searched the existing issues

### Is your feature request related to a problem? Please describe the problem.

I am trying to use Rush as my package manager (similar to the existing solutions for Yarn, Pnpm, and Npm), but there is no first-party method to call. This is problematic, as Rush explicitly doesn't like using `pnpm install` or `npm install`. A bit funny, considering that Rush is Microsoft's monorepo solution.

### Describe the solution you'd like

I'd like to see better support for monorepos. My ideal solution would be
```
builder.AddRushApp("myRushApp").WithPnpm()
```

### Additional context

_No response_