Update InjectAutoreloadMiddleware to be compatible with starlette >= 0.35.0

[schloerke]

Related: Kludex/starlette#2381

Do not merge until motivation for #1009 is resolved

[wch]

I think the root of this problem is:
starlette claims that you can use types from starlette or types from asgiref, where the latter are more rigorous (and what we have in the existing code). They show the two methods here:
https://github.com/encode/starlette/blob/39dccd9/docs/middleware.md#type-annotations

However, in Kludex/starlette#2381, the explicit types they added are the starlette types, not the asgiref types, and that's why we started getting type-checking errors.

The change in this PR makes it so, on the outside, it uses the starlette types, but on the inside, it uses the asgiref types.

I think it would be better if the external interface supported both types.