[Bug] context.thread_local_storage.invocation_id does not correlate thread logs in Application Insights on Python 3.13

### Expected Behavior

According to the docs, setting context.thread_local_storage.invocation_id
inside a background thread enables log correlation for that thread:
https://learn.microsoft.com/en-us/azure/azure-functions/functions-reference-python#log-custom-telemetry

After calling:
context.thread_local_storage.invocation_id = context.invocation_id

...all logging.info() calls from that thread should appear in Application
Insights correlated to the function invocation (same InvocationId).

### Actual Behavior

On Python 3.13, [THREAD] logs are completely absent from Application Insights.
[MAIN] logs appear correctly. The identical code works on Python 3.12.

Python 3.12 ✅
"Logging from main handler" → appears, InvocationId=37b57bfd-...
"Logging from a background thread" → appears, InvocationId=37b57bfd-...

Python 3.13 ❌
"Logging from main handler" → appears, InvocationId=48b27079-...
"Logging from a background thread" → ABSENT from App Insights entirely

### Steps to Reproduce

1. Deploy Azure Function App with Python 3.13, Azure Functions Runtime v4, Dedicated plan
2. Use the code below (async HTTP trigger + asyncio.to_thread)
3. Trigger the function via HTTP
4. Check Application Insights traces — background thread log is missing
5. Redeploy the same code with Python 3.12 — background thread log appears correctly

### Relevant code being tried

```shell
import azure.functions as func
import logging
import asyncio

app = func.FunctionApp(http_auth_level=func.AuthLevel.ANONYMOUS)

def work(context: func.Context):
context.thread_local_storage.invocation_id = context.invocation_id
logging.info("Logging from a background thread")

@app.route(route="test")
async def test_async(req: func.HttpRequest, context: func.Context) -> func.HttpResponse:
await asyncio.to_thread(work, context)
logging.info("Logging from main handler")
return func.HttpResponse("ok")
```

### Relevant log output

```shell

```

### requirements.txt file

```shell
azure-functions
```

### Where are you facing this problem?

Production Environment (explain below)

### Function app name

_No response_

### Additional Information

Root cause: azure-functions-runtime (used on Python 3.13) has its own separate
threading.local object for log routing. context.thread_local_storage points to
azure-functions-worker's threading.local — a different object that the new
runtime's logging proxy never reads.

Workaround (confirmed working on Python 3.13):

from azure_functions_runtime.utils.executor import invocation_id_cv

def work():
logging.info("Logging from a background thread")

@app.route(route="test")
async def test_async(req, context):
invocation_id_cv.set(context.invocation_id) # copied by asyncio.to_thread
await asyncio.to_thread(work)

asyncio.to_thread copies ContextVars automatically, so the proxy finds the
invocation_id correctly.

Note: invocation_id_cv is an internal API — a public API for this use case
would be appreciated.

Comienza reproduciendo el disparador HTTP async con asyncio.to_thread en Python 3.12 y 3.13; después, inspecciona el workaround de invocation_id_cv en azure_functions_runtime.utils.executor y el uso de context.thread_local_storage.invocation_id. Se considera terminado cuando los logs de los hilos en segundo plano aparecen en Application Insights con el mismo InvocationId en Python 3.13 mediante una API compatible.

Escrito por el modelo de indexación a partir del texto del issue.