No logs from CMD when Python file can't load in Docker image

#### Is your question related to a specific version? If so, please specify:

Docker image:

```
mcr.microsoft.com/azure-functions/python:4-python3.14
```

#### What language does your question apply to? (e.g. C#, JavaScript, Java, All)

Python

#### Question

With a Dockerfile like:
```
FROM mcr.microsoft.com/azure-functions/python:4-python3.14

ENV AzureWebJobsScriptRoot=/home/site/wwwroot \
AzureFunctionsJobHost__Logging__Console__IsEnabled=true

COPY requirements.txt /
RUN pip install -r /requirements.txt

COPY function_app.py /home/site/wwwroot/
```

When add this to my `function_app.py`:

```
from azure.identity.aio import DefaultAzureCredential
credential = DefaultAzureCredential()
```

Running goes from this:
```
WEBSITES_INCLUDE_CLOUD_CERTS is not set to true.
info: Host.Triggers.Warmup[0]
Initializing Warmup Extension.
info: Host.Startup[503]
...
info: Host.Startup[413]
Host started (180ms)
info: Host.Startup[0]
Job host started
Hosting environment: Production
Content root path: /
Now listening on: http://[::]:80
Application started. Press Ctrl+C to shut down.
```

to this:

```
WEBSITES_INCLUDE_CLOUD_CERTS is not set to true.
Hosting environment: Production
Content root path: /
Now listening on: http://[::]:80
Application started. Press Ctrl+C to shut down.
```

And trying to hit any endpoint results on `Function host is not running.`.

---

In my case the underlying issue was not having `aiohttp` installed,
but it would be nice to have **any log output whatsoever**.

It doesn't even tell me there was a problem with `function_app.py`,
let alone what the problem was.

Invoking manually in the container I could see:

```
root@09ce4f921168:/# python /home/site/wwwroot/function_app.py
Traceback (most recent call last):
File "/opt/python/3/lib/python3.14/site-packages/azure/core/pipeline/transport/__init__.py", line 90, in __getattr__
from ._aiohttp import AioHttpTransport
File "/opt/python/3/lib/python3.14/site-packages/azure/core/pipeline/transport/_aiohttp.py", line 49, in
import aiohttp
ModuleNotFoundError: No module named 'aiohttp'
```

Can we have this output sent to stdout?

Reproduce the failure using the shown Dockerfile and function_app.py, with the missing aiohttp dependency, then trace how the host handles errors while loading the Python file. Check that the import traceback and a clear indication that function_app.py failed to load are emitted to stdout, and verify that endpoint requests no longer fail silently.

Written by the indexing model from the issue text.