Improve API structure + put non-async handlers properly

[PawelPeczek-Roboflow]

Search before asking

• I have searched the Inference issues and found no similar bug report.

Bug

The HTTP API module requires re-design. It is large and contains plenty of handlers. Some handlers (running non-asyncio code) are marked async improperly, potentially making the API less performant (fastapi handles both async and non-async handlers, just stamps need to be placed properly). We have this mistake by the virtue of error handling wrapper which is async-first.
Please re-design API as maintenance activity.

Environment

No response

Minimal Reproducible Example

No response

Additional

No response

Are you willing to submit a PR?

• Yes I'd like to help by submitting a PR!