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/alembic/versions/fc01_add_pending_task_lane.py

@@ -0,0 +1,30 @@
+"""add pending_task_lane to ai_sessions
+
+Revision ID: fc01a1b2c3d4
+Revises: fb1481317ff6
+Create Date: 2026-03-27
+"""
+from alembic import op
+import sqlalchemy as sa
+from sqlalchemy.dialects.postgresql import JSONB
+
+revision = "fc01a1b2c3d4"
+down_revision = "fb1481317ff6"
+branch_labels = None
+depends_on = None
+
+
+def upgrade() -> None:
+    op.add_column(
+        "ai_sessions",
+        sa.Column(
+            "pending_task_lane",
+            JSONB,
+            nullable=True,
+            comment="Current task lane state: {questions: [...], actions: [...]}",
+        ),
+    )
+
+
+def downgrade() -> None:
+    op.drop_column("ai_sessions", "pending_task_lane")