feat(escalations): close out plan-locked wedge polish

Four items from the design-plan audit, all flagged as locked-design or
Codex corrections, shipped together so the GTM demo path covers them
end-to-end before bug bash.

1. Live AI assessment refresh on the magic-moment screen. Backend already
   publishes handoff_assessment_ready when enrich_escalation_async commits;
   wire the frontend listener so the senior sees the assessment populate
   without a manual reopen. New event type + onAssessmentReady handler on
   streamEscalations; AssistantChatPage opens a scoped SSE subscription
   whenever it tracks a handoff missing its assessment, refetches on match,
   and replaces magicHandoff / overlayHandoff in place. Closes the loop on
   the async-assessment commit e8ba74e.

2. Suggested-step chips below the chat input. Locked design from the plan
   (Codex correction). Chip strip renders above the composer post-claim
   when ai_assessment_data.suggested_steps[] is non-empty. Click prefills
   the input and focuses; first send or explicit X hides for the session.

3. Unread 6px dot on EscalationQueue cards. localStorage-persisted seen
   set (rf-escalation-seen, capped 200). Dot top-right when not seen.
   Cleared on open (card click) or claim (Pick Up) — NOT on hover, per
   Codex correction. Pick Up stops propagation so it doesn't double-fire.

4. Race-condition toast on claim conflict. The /claim endpoint previously
   silently overwrote claimed_by — both seniors thought they owned the
   session. New HandoffAlreadyClaimedError carries the winner's id/name/
   timestamp; claim_session rejects different-user re-claims (same-user is
   idempotent for double-click safety); endpoint returns 409 with
   structured detail. AssistantChatPage.handleStartHere extracts and
   surfaces "Already claimed by {name} {time_ago}." via toast, drops
   ?pickup=true, dismisses magic-moment so the loser flows back to queue.

Tests: 2 new unit tests in test_handoff_manager.py (conflict raises,
same-user idempotent). Full handoff + escalation suite (34 tests) green.
Frontend tsc -b clean.

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

backend/app/api/endpoints/session_handoffs.py

@@ -22,7 +22,7 @@ from app.core.escalation_bus import bus as escalation_bus
 from app.models.user import User
 from app.models.ai_session import AISession
 from app.models.session_handoff import SessionHandoff
-from app.services.handoff_manager import HandoffManager
+from app.services.handoff_manager import HandoffAlreadyClaimedError, HandoffManager
 from app.schemas.session_handoff import (
     HandoffCreateRequest,
     HandoffResponse,
@@ -129,6 +129,19 @@ async def claim_handoff(
             handoff_id=handoff_id,
             claiming_user_id=current_user.id,
         )
+    except HandoffAlreadyClaimedError as e:
+        # Loser of the race — the API surfaces structured detail so the
+        # client can render "Already claimed by {name} {time_ago}" without
+        # a follow-up fetch.
+        raise HTTPException(
+            status_code=status.HTTP_409_CONFLICT,
+            detail={
+                "error": "already_claimed",
+                "claimed_by_id": str(e.claimed_by_id),
+                "claimed_by_name": e.claimed_by_name,
+                "claimed_at": e.claimed_at.isoformat(),
+            },
+        )
     except ValueError as e:
         raise HTTPException(status_code=404, detail=str(e))