fix(gateway): emit agent:start on interrupt/drain follow-up turns

[Couiz]

Problem

The main message dispatch emits the agent:start hook before running the agent, but the interrupt/drain follow-up path in _run_agent promotes a queued message straight into the recursive _run_agent call without emitting agent:start.

With busy_input_mode: interrupt, a message typed while the agent is busy interrupts the run, is queued in _pending_messages, and later drains as a follow-up turn — so every hook listening on agent:start (SessionStart-style integrations, activity loggers, visualizers) silently misses these turns. The hook system is fine; the gateway just never fires the event on this path. agent:start currently fires only in the main dispatch.

Fix

Emit agent:start once on the drain path, immediately before the follow-up _run_agent call, mirroring the main-dispatch payload but built from the drain-site variables (next_source, and the final, already-transcribed next_message). It sits after every discard guard (stale /goal continuation, _prepare_inbound_message_text returning None), inside the same try block as the main-path emit, so it:

• fires exactly once per turn, and only when the follow-up actually proceeds to _run_agent;
• carries the transcript for voice follow-ups, not the raw-audio placeholder;
• truncates message to 500 chars like the main path;
• shares the main path's exception parity.

15 lines, surgical — the main dispatch is untouched and _run_agent's signature is unchanged.

Tests

New tests/gateway/test_drain_emits_agent_start.py drives the real drain path via _pending_messages (mocking only transcription), asserting:

• one agent:start emit with a main-path-shaped payload for text follow-ups;
• the voice follow-up payload carries the transcript, never the audio path;
• message truncated to 500 chars;
• no emit on the two discard branches (_prepare→None, stale /goal continuation).

RED before the fix (3 positive tests fail, 2 discard-guards pass), GREEN after. The full gateway interrupt/drain/pending/restart suite stays green (102 passed). ruff check passes. No lockfile or unrelated changes.

[Couiz]

Consolidated into #39126 — the three changes (agent:start on drain, trigger/depth tagging, agent:end on drain) are one coherent concern, and the agent:end fix's payload carries the trigger/interrupt_depth tagging, so they aren't cleanly separable. A single PR off fresh main reviews better than three stacked PRs across diverging bases. Closing in favor of #39126.