FastAPI: Context change in sync route does not appear in background tasks

Describe your environment

OS: Ubuntu
Python version: 3.11.0

Package version:
opentelemetry-api==1.34.1
opentelemetry-sdk==1.34.1
opentelemetry-instrumentation-fastapi==0.55b1

What happened?

When having a sync route in FastAPI and launching a background task, the changes done to the context do not appear in the context of the background task.

Steps to Reproduce

from fastapi import BackgroundTasks, FastAPI
from opentelemetry import context, trace
from opentelemetry.context import set_value
from opentelemetry.instrumentation.fastapi import FastAPIInstrumentor
from opentelemetry.sdk.resources import SERVICE_NAME, Resource
from opentelemetry.sdk.trace import TracerProvider
from opentelemetry.sdk.trace.export import BatchSpanProcessor, ConsoleSpanExporter

app = FastAPI()

# =========================================================================== #
# Optional: Bug is reproducible with or without setuping the resource, tracer
# provider and FastAPI instrumentor,
resource = Resource.create(attributes={SERVICE_NAME: "pricing-recommendation-engine"})

provider = TracerProvider(resource=resource)
trace.set_tracer_provider(provider)

# provider.add_span_processor(BatchSpanProcessor(ConsoleSpanExporter()))

FastAPIInstrumentor().instrument_app(app)
# =========================================================================== #


def my_background_task():
    print(context.get_current())


def add_test_value_to_context():
    ctx = context.get_current()
    ctx = set_value("test_key", "test_value", context=ctx)
    context.attach(ctx)


@app.get("/sync-endpoint")
def sync_endpoint(background_tasks: BackgroundTasks):
    print(context.get_current())
    add_test_value_to_context()
    print(context.get_current())
    background_tasks.add_task(my_background_task)
    return "Hello, World!"


@app.get("/async-endpoint")
async def async_endpoint(background_tasks: BackgroundTasks):
    print(context.get_current())
    add_test_value_to_context()
    print(context.get_current())
    background_tasks.add_task(my_background_task)
    return "Hello, World!"

uvicorn fastapi_context_bug:app

On endpoint /sync-endpoint, we get this:

{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /sync-endpoint", context=SpanContext(trace_id=0x3d1bdba09cbb92564db952045e92ab94, span_id=0x93ec8565cd311ed4, trace_flags=0x01, trace_state=[], is_remote=False))}
{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /sync-endpoint", context=SpanContext(trace_id=0x3d1bdba09cbb92564db952045e92ab94, span_id=0x93ec8565cd311ed4, trace_flags=0x01, trace_state=[], is_remote=False)), 'test_key': 'test_value'}
INFO:     127.0.0.1:45994 - "GET /sync-endpoint HTTP/1.1" 200 OK
{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /sync-endpoint", context=SpanContext(trace_id=0x3d1bdba09cbb92564db952045e92ab94, span_id=0x93ec8565cd311ed4, trace_flags=0x01, trace_state=[], is_remote=False))}

On endpoint /async-endpoint, we get this:

{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /async-endpoint", context=SpanContext(trace_id=0xf1009be126c6edf441c7f465fcc05e7e, span_id=0xfa1e818754376b97, trace_flags=0x01, trace_state=[], is_remote=False))}
{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /async-endpoint", context=SpanContext(trace_id=0xf1009be126c6edf441c7f465fcc05e7e, span_id=0xfa1e818754376b97, trace_flags=0x01, trace_state=[], is_remote=False)), 'test_key': 'test_value'}
INFO:     127.0.0.1:48510 - "GET /async-endpoint HTTP/1.1" 200 OK
{'current-span-b13884d6-004f-41b3-84b0-8704e8205ff6': _Span(name="GET /async-endpoint", context=SpanContext(trace_id=0xf1009be126c6edf441c7f465fcc05e7e, span_id=0xfa1e818754376b97, trace_flags=0x01, trace_state=[], is_remote=False)), 'test_key': 'test_value'}

Expected Result

The sync route should behave as the async route.

Actual Result

See above.

Additional context

No response

Would you like to implement a fix?

None

Start at FastAPIInstrumentor and trace how sync and async routes run background tasks and propagate context. Reproduce the difference between /sync-endpoint and /async-endpoint, then add coverage showing that the sync route preserves the changed context in its background task and run the relevant instrumentation tests.