Reorganize hq CLI: OutputSink context manager, section ordering, and cleanups

Introduces OutputSink to own the output lifecycle (stream/accumulate/flush),
replacing the mutable json_accumulator parameter threading. Reorganizes all
definitions into dependency-ordered sections (constants → helpers → query
dispatch → output → execution → CLI). Deduplicates file reading via
_read_input, simplifies _extract_location with a loop, collapses redundant
except blocks, and removes dead code.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: kkozik-amplify