feat(analytics): add escalation time-to-first-action metric endpoint

GET /api/v1/analytics/flowpilot/escalations?period={7d,30d,90d}

Computes the in-product wedge metric for Escalation Mode: average / median /
p95 seconds between SessionHandoff.claimed_at and the first ai_session_step
created on the same session after that timestamp. Account-scoped, role-gated
to engineer-or-admin.

The metric is intentionally NOT called "minutes recovered" — that's the
two-metric framing locked by /codex review: this in-product number must be
paired with manual baseline (the verbal-handoff stopwatch from The Assignment)
to produce the savings claim. Schema's `metric_definition` field surfaces the
disclaimer in every response so callers don't oversell it.

Implementation notes:
- Uses correlated scalar subquery for first-step-after-claim per handoff,
  aggregates avg/median/p95 in Python (~1k rows/account/month is well within
  budget; cleaner than percentile_cont gymnastics in SQL)
- Excludes unclaimed handoffs (claimed_at IS NULL)
- Counts claimed-but-no-action handoffs in n_handoffs_claimed but not in
  n_handoffs_with_action — surfaces the conversion-rate signal
- Floors negative deltas at 0 to handle clock-drift edge cases

Tests cover happy path, zero-data, claimed-but-no-action accounting, period
window filtering, multi-handoff aggregation, multi-tenant isolation (Phase 4
RLS landmine pattern), viewer-role 403 gate, and period validation. 9 tests,
all green. No regressions in existing handoff_manager / session_handoffs
suites.

First piece of the Approach A wedge build per
docs/plans/2026-04-27-escalation-mode-wedge-design.md. Unblocks the queue
stat-card and the analytics page.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

backend/app/schemas/flowpilot_analytics.py

@@ -124,3 +124,26 @@ class FlowPilotDashboard(BaseModel):
     confidence_breakdown: ConfidenceBreakdown
     knowledge_coverage: KnowledgeCoverage
     psa_metrics: PsaMetrics | None = None
+
+
+class EscalationMetrics(BaseModel):
+    """In-product time-to-first-action metric for the Escalation Mode wedge.
+
+    NOTE: this is the *in-product* metric (post-claim time-to-first-action). The
+    "minutes recovered" sales claim requires a manual baseline measurement of the
+    pre-Escalation-Mode verbal-handoff time. See
+    docs/plans/2026-04-27-escalation-mode-wedge-design.md for the two-metric
+    framing — do not roll this number alone into "minutes recovered."
+    """
+
+    period: str
+    n_handoffs_claimed: int
+    n_handoffs_with_action: int
+    avg_seconds_to_first_action: float | None = None
+    median_seconds_to_first_action: float | None = None
+    p95_seconds_to_first_action: float | None = None
+    metric_definition: str = (
+        "elapsed_seconds(first ai_session_step in session where "
+        "created_at > SessionHandoff.claimed_at) — measures post-claim activity "
+        "lag, NOT verbal-handoff savings. Pair with manual baseline."
+    )