Can't add span processor in post_fork when using `initialize()`

Describe your environment

OS: Ubuntu
Python version: Python 3.13.37
API version: "opentelemetry-distro[otlp]>=0.57b0"

What happened?

this is in my gunicorn post_fork:

def post_fork(server: Arbiter, worker: CanvasUvicornWorker) -> None:
    from opentelemetry.instrumentation.auto_instrumentation import initialize
    initialize()

    PYROSCOPE_URL = os.getenv("PYROSCOPE_URL")
    PYROSCOPE_USER = os.getenv("PYROSCOPE_USER")
    PYROSCOPE_PASSWORD = os.getenv("PYROSCOPE_PASSWORD")

    if PYROSCOPE_URL and PYROSCOPE_USER and PYROSCOPE_PASSWORD:
        pyroscope.configure(
            application_name="home-app",
            server_address=PYROSCOPE_URL,
            basic_auth_username=PYROSCOPE_USER,
            basic_auth_password=PYROSCOPE_PASSWORD,
            sample_rate=100,  # default is 100
            detect_subprocesses=True,
            oncpu=True,  # report cpu time only; default is True
            gil_only=True,
            enable_logging=True,
            tags={
                "customer": os.getenv("CUSTOMER_IDENTIFIER"),
            },
        )

        tp = trace.get_tracer_provider()
        tp.add_span_processor(PyroscopeSpanProcessor())

        tr = tp.get_tracer("probe")

        with tr.start_as_current_span("pyro-probe"):
            pass

My pyro-probe span does have a pyroscope.span.id, but none of the spans generated from the auto-instrumentation do.

What is the correct way to add a span processor to the tracer provider that the initialize() method generates?

Steps to Reproduce

See above code.

Expected Result

All spans contain a pyroscope.span.id (this is specific to this span processor, but the general expected result is that the span processor runs for all spans, not just ones created in this block).

Actual Result

Any span generated from auto-instrumentation does not have the span processor added afterwards run.

Additional context

No response

Would you like to implement a fix?

None

Tip

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Start at the auto_instrumentation.initialize() entry point shown in the report and trace how it creates or configures the tracer provider during the Gunicorn post_fork hook. Reproduce the example with the PyroscopeSpanProcessor, then verify that spans from auto-instrumented components receive the processor as well as the manually created probe span.