AlwaysOn with AuthLevel.FUNCTION fails - need guidance for FastAPI + authenticated warmup

Related to #9109 which identified that AlwaysOn uses `/admin/warmup` endpoint.

## Issue
We're seeing 401 errors with AlwaysOn when using `AuthLevel.FUNCTION` with FastAPI on Azure Functions. The `/admin/warmup` endpoint used by AlwaysOn doesn't include function keys, causing authentication failures.

## Current setup
```python
# function_app.py
import azure.functions as func
from fastapi import FastAPI

fast_app = FastAPI()
app = func.AsgiFunctionApp(app=fast_app, http_auth_level=func.AuthLevel.FUNCTION)
```

- Premium plan with AlwaysOn enabled
- Function authentication level set to FUNCTION

## Attempted solutions
1. Added web.config to scripts folder:
```xml

```
Result: Configuration does not get deployed to wwwroot

2. Tried `WEBSITE_WARMUP_PATH` setting
Result: Documentation confirms this doesn't affect AlwaysOn path

## Logs
```
2024-04-04T05:58:14Z [Information] Executing StatusCodeResult, setting HTTP status code 401
```

## Key Questions
1. Is there a way to set different auth levels per route while keeping app-level auth?
2. Can we configure AlwaysOn to use function keys?
3. What's the recommended approach for FastAPI apps that need both security and AlwaysOn?

## Environment
- Python 3.11
- Azure Functions runtime v4
- FastAPI on Azure Functions
- Authentication Level: FUNCTION
- Hosting: Premium plan
### extra context
* https://www.thebestcsharpprogrammerintheworld.com/2018/08/23/how-to-optimize-azure-app-service-alwayson-cold-start-warm-up-request/
* https://learn.microsoft.com/en-us/azure/app-service/reference-app-settings?tabs=kudu%2Cdotnet

Please provide guidance on the recommended approach to handle this authentication scenario without compromising security by switching to `AuthLevel.ANONYMOUS`.

Start with function_app.py and the AsgiFunctionApp authentication configuration, then trace how the /admin/warmup request is handled. Review the reported web.config deployment result, WEBSITE_WARMUP_PATH behavior, and the 401 log. Done means establishing and documenting a supported approach for authenticated FastAPI warmup without weakening the app's security.

Written by the indexing model from the issue text.