Starlette instrumentation tests fail recent versions `starlette >= 0.15.0`

[aabmass]

Originally posted by @aabmass in #3304 (comment)

Only really ancient versions of starlette seem to be working with opentelemetry-insturmentation-starlette. The tests fail if you increase the version range because of an issue with capturing custom headers. See thread for more context.

[Kludex]

The reason is that we adopted anyio in Starlette on that version.

That said, I don't think it makes sense to maintain <0.15, nor anything close to that. 0.15.0 is from June 23, 2021. In the ASGI ecosystem, that is pretty old already.

[aabmass]

I agree we should increase the minimum version. Is this something you'd be willing to work on?

[Kludex]

I don't think I'll have time soon. If someone else wants to try, I can review it. Otherwise, we can wait till I have a bit more time.