Flip the live callers (new_chat_routes + gateway/agent_invoke) from the
legacy monolithic app.tasks.chat.stream_new_chat to the side-by-side
app.tasks.chat.streaming.flows orchestrators.
Adds a byte-for-byte differential parity test driving BOTH implementations
on identical, fully-deterministic glue inputs (frozen time/uuid, stubbed
LLM/persistence/agent seams). All glue paths are byte-identical:
* new: auto-pin failure, LLM-load failure, persist-user fail,
persist-assistant fail (full initial-frame ordering + handshake),
pre-stream exception (top-level except path)
* resume: persist-assistant fail
The differential test also surfaced one INTENTIONAL divergence: on a resume
turn whose auto-pin / LLM-load fails, the monolith crashes with
UnboundLocalError (_resume_premium_request_id read in finally before its
post-early-return definition); the flows version emits a clean terminal
error. The flows path is therefore byte-identical or strictly more correct.
The agent-content stream itself is shared, unforkable code
(stream_output -> EventRelay) so it cannot diverge.
Monolith + old parity test deletion follows in a separate commit.
