Refactor and optimize processing after zipper merge.

[grzkv]

We need to do the following:

• Unified abstraction of a request. Now there is a set of different ones because zipper was separated.
• Clear trace of the request processing timeline.
• Stop using context to pass values during processing.
• Simplify the processing pipeline if possible.
• (needs discussion) Cancel the whole request if a single sub-request failed.