Click Instrumentation Bypass Issue

Describe your environment

OS: Fedora 42
Python version: 3.12
Package version: 0.57b0

What happened?

I was running a FastAPI application using python -m uvicorn instead of using the uvicorn executable directly and was seeing all of my requests going under a top-level python -m uvicorn span.

Steps to Reproduce

Attempt to run a FastAPI application using python -m uvicorn instead of uvicorn.

Expected Result

Each separate request should get it's own span instead of every request's span going under a top-level span.

Actual Result

Each separate request's span goes under a single top-level span when starting with python -m uvicorn

Additional context

I did some pre-emptive looking into this problem and have found that it is caused by the click Instrumentation failing to sniff out that it is being ran in a FastAPI application.

Would you like to implement a fix?

Yes

Tip

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Reproduce the issue by starting the FastAPI application with python -m uvicorn and compare it with the uvicorn executable. Inspect the Click instrumentation's FastAPI detection and add a regression test if the repository provides one; done means each request has its own span rather than being nested under one top-level span.