## Problem
https://github.com/neondatabase/cloud/issues/11051
additionally, I felt like the http logic was a bit complex.
## Summary of changes
1. Removes timeout for HTTP requests.
2. Split out header parsing to a `HttpHeaders` type.
3. Moved db client handling to `QueryData::process` and
`BatchQueryData::process` to simplify the logic of `handle_inner` a bit.