Fix request `Content-Type` header checking in servers (#3690)

This fixes two bugs:

1. `Content-Type` header checking was succeeding when no `Content-Type`
   header was present but one was expected.
2. When a shape was `@httpPayload`-bound, `Content-Type` header checking
   occurred even when no payload was being sent. In this case it is not
   necessary to check the header, since there is no content.

Code has been refactored and cleaned up. The crux of the logic is now
easier to understand, and contained in `content_type_header_classifier`.

## Checklist
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rather than leaving it unchecked -->
- [x] I have updated `CHANGELOG.next.toml` if I made changes to the
smithy-rs codegen or runtime crates

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