feat: persist task lane across submits and session reloads

Task lane questions/actions are now saved to a pending_task_lane JSONB
column on ai_sessions, restoring them on session switch or page reload.
Partial submit no longer force-clears the lane — the AI response
controls what stays. Also removes redundant "New Session" button from
the sidebar (dashboard already provides this).

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

backend/app/models/ai_session.py

@@ -209,6 +209,10 @@ class AISession(Base):
         JSONB, nullable=False, default=list,
         comment="Full LLM message history for context continuity",
     )
+    pending_task_lane: Mapped[Optional[dict[str, Any]]] = mapped_column(
+        JSONB, nullable=True,
+        comment="Current task lane state: {questions: [...], actions: [...]}",
+    )
 
     # ── Branching ──
     is_branching: Mapped[bool] = mapped_column(