feat(gateway): tag agent:start payload with turn trigger + interrupt_depth

[Couiz]

What

agent:start is emitted at two sites in gateway/run.py — the main inbound dispatch and the interrupt/drain follow-up path in _run_agent — and both previously emitted an identical payload shape. Hooks (voice-echo, activity loggers, visualizers) therefore could not distinguish a fresh user turn from an interrupt-driven follow-up turn.

This adds two discriminator fields to the agent:start payload at both sites:

• trigger — a string (not a bool, so future turn kinds like "goal" / "schedule" extend the contract without breaking it): "message" on the main dispatch, "interrupt" on the drain follow-up. Hooks read it backward-compatibly via context.get("trigger", "message").
• interrupt_depth — an int: 0 on the main dispatch (a fresh turn is never an interrupt); _interrupt_depth + 1 on the drain path, matching the depth handed to the recursive _run_agent call (first interrupt → 1, interrupt-of-an-interrupt → 2, …).

Both payloads stay shape-consistent (7 keys); no existing key changes. The drain emit still sits after every discard guard (stale /goal, transcription→None), so it fires once per turn only when the follow-up actually proceeds to the agent.

Tests

• test_drain_emits_agent_start.py: updated the exact-dict assertion to the new shape; added a first-level (depth == 1) and a nested (_interrupt_depth=1 → depth == 2) case driving the real _run_agent drain path. The existing no-emit-on-discard tests are unchanged and still pass.
• test_agent_start_trigger.py (new): the main-dispatch emit lives ~630 lines deep behind session-store/DB/env I/O, so rather than mock that world this statically inspects the actual dict literal handed to hooks.emit("agent:start", …) and pins trigger="message" / interrupt_depth=0.

Notes

Depends on #37269 (the drain-emit fix this builds on). The first commit in this PR is that fix; it will drop out once #37269 merges.

[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.