Automatic instrument with `flask run` versus `python` results in `status_code` being `UNSET`

Describe your environment

Python 3.9+ with OTel supported Flask/Werkzeug

Steps to reproduce

Follow the steps here https://opentelemetry.io/docs/instrumentation/python/getting-started/ and check the JSON output

What is the expected behavior?

    ...
    "status": {
        "status_code": "OK"
    },
    ...

Like when following directions here: https://opentelemetry.io/docs/instrumentation/python/automatic/example/

What is the actual behavior?

    ...
    "status": {
        "status_code": "UNSET"
    },
    ...

Additional context

It appears when flask run is used, the status_code is not set properly even though the HTTP status code is set properly ("http.status_code": 200). If you start the app with python it works properly.