fix(escalations): bump assessment timeout, surface picked-up sessions in sidebar

Two field-reported issues from live wedge testing.

ESCALATION_AI_ASSESSMENT_TIMEOUT_SECONDS bumped 5s → 15s. The 5s bound
fired too aggressively against the Sonnet diagnostic assessment prompt;
~4-8s is typical but tail latency hits 12-14s. The fallback "Assessment
unavailable — model didn't respond in time" placeholder was showing on
the magic-moment screen for two consecutive escalations, which kills
the demo. 15s keeps the click-path bounded but lets the typical case
return real content. Real fix is async generation (kick off, persist
when done, surface "still computing" with refresh) — captured as a
follow-up; bumping the bound is the right call for the wedge demo.

list_sessions now matches escalated_to_id == current_user.id alongside
the existing user_id and escalation_package.picked_up_by clauses. The
unified HandoffManager.claim_session sets escalated_to_id but doesn't
write the legacy picked_up_by JSONB key, so picked-up sessions never
showed in the senior's chat list — the senior would land on the
session detail (active chat) but the sidebar showed only their other
unrelated sessions. User reported this as "4 different versions of the
session in the chat history section" — they were actually 4 unrelated
empty sessions the senior owned, plus the picked-up session was just
invisible. Backend tests still 94/94.

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

backend/app/core/config.py

@@ -111,7 +111,14 @@ class Settings(BaseSettings):
     GOOGLE_AI_API_KEY: Optional[str] = None
     AI_MODEL_GEMINI: str = "gemini-2.5-flash"
     AI_MODEL_ANTHROPIC: str = "claude-sonnet-4-6"
-    ESCALATION_AI_ASSESSMENT_TIMEOUT_SECONDS: int = 5
+    # 15s is generous for the click-path; Claude usually returns a 500-token
+    # diagnostic in 4-8s but tail latency on the assessment prompt has hit
+    # 12-14s in the field. Going below this leaves too many escalations with
+    # the "Assessment unavailable — model didn't respond in time" placeholder
+    # the senior sees on the magic-moment screen. Real fix is async generation
+    # (kick off, persist when done, surface "still computing" with refresh) —
+    # that's a follow-up; bumping the bound keeps the wedge demo coherent.
+    ESCALATION_AI_ASSESSMENT_TIMEOUT_SECONDS: int = 15
 
     # Model tier routing — maps action types to model tiers
     AI_MODEL_TIERS: dict[str, str] = {