Remove usage of async_closure

[taiki-e]

Description

Motivation and Context

async_closure won't be stable any time soon and are equivalent to closures which return async blocks.

Related: rust-lang/futures-rs#1716 (comment)

How Has This Been Tested?

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)

Checklist:

• My change requires a change to the documentation.
• I have updated the documentation accordingly.
• I have read the CONTRIBUTING document.
• I have added tests to cover my changes.
• All new and existing tests passed.

[secretfader]

I recently added the async_closure feature flag to http-service during an effort to fix builds on recent nightlies, and I'm happy to remove it if this is merged. Anything that moves us towards stability sooner rather than later gets my vote. 👍

[fairingrey]

This looks pretty simple enough, thanks for the help! 👍

I'll be looking at updating other libraries in rust-async to follow this change soon, probably.

[secretfader]

Since this feature gate is currently deferred, I favor moving other libraries to match the standard set by this PR.