[FastAPI] exception handler always has span_id is 0

Describe your environment

OS: Ubuntu
Python version: 3.12

What happened?

When an exception is raised and handled by the exception_handler, the span_id printed is always 0. However, the span_idprinted in the middleware is correct.

Steps to Reproduce

from opentelemetry.instrumentation.fastapi import FastAPIInstrumentor
from fastapi.responses import JSONResponse
from fastapi import FastAPI, Request
from opentelemetry.trace import get_current_span
from opentelemetry import trace
from opentelemetry.sdk.trace import TracerProvider
from opentelemetry.sdk.trace.export import BatchSpanProcessor
from opentelemetry.exporter.otlp.proto.grpc.trace_exporter import OTLPSpanExporter

otlp_url = 'http://localhost:4317'

trace.set_tracer_provider(TracerProvider())
span_exporter = OTLPSpanExporter(endpoint=otlp_url)
span_processor = BatchSpanProcessor(span_exporter)
trace.get_tracer_provider().add_span_processor(span_processor)


app = FastAPI()


@app.exception_handler(Exception)
def exception_handler(request: Request, exception: Exception):
    print('exception_handler', get_current_span().get_span_context().span_id)

    return JSONResponse(
        status_code=500,
        content={"message": "Internal server error"},
    )


@app.middleware("http")
async def middleware(request: Request, call_next):
    print('middleware', get_current_span().get_span_context().span_id)

    response = await call_next(request)
    return response


@app.get("/")
def read_root():
    raise Exception("error")


FastAPIInstrumentor.instrument_app(app)

Expected Result

middleware 1234
exception_handler 1234

Actual Result

middleware 1234
exception_handler 0

Additional context

No response

Would you like to implement a fix?

None

Start with the FastAPIInstrumentor instrumentation and reproduce the issue using the provided exception_handler and middleware example. Compare the active span context at both points and trace how exception handling affects it; done means the handler reports the same nonzero span_id as the middleware.