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>

frontend/src/components/layout/Sidebar.tsx

@@ -5,7 +5,7 @@ import {
   LayoutGrid, Clock, AlertTriangle, GitBranch, Code2, Wand2,
   ListChecks, Download, BarChart3,
   Settings, Pin, PinOff,
-  Plus, History, FileText,
+  History, FileText,
 } from 'lucide-react'
 import { cn } from '@/lib/utils'
 import { useUserPreferencesStore } from '@/store/userPreferencesStore'
@@ -363,17 +363,6 @@ export function Sidebar() {
         style={{ background: 'var(--color-bg-sidebar)', borderRight: '1px solid var(--color-border-default)' }}
         onWheel={handleWheel}
       >
-        {/* New Session button */}
-        <div className="px-3 pt-3 pb-1">
-          <Link
-            to="/"
-            className="flex items-center justify-center gap-2 w-full rounded-lg bg-amber-400/15 py-2.5 text-sm font-semibold text-amber-400 hover:bg-amber-400/25 transition-colors"
-          >
-            <Plus size={16} strokeWidth={2} />
-            New Session
-          </Link>
-        </div>
-
         {/* Pinned sidebar content */}
         <div className="px-3 py-2 space-y-0.5">
           {sections.map((section, si) => (
@@ -420,18 +409,6 @@ export function Sidebar() {
         style={{ background: 'var(--color-bg-sidebar)', borderRight: '1px solid var(--color-border-default)', width: '72px' }}
         onWheel={handleWheel}
       >
-        {/* New Session button */}
-        <div className="w-full px-2 pt-4 pb-2">
-          <Link
-            to="/"
-            className="flex flex-col items-center justify-center w-full rounded-lg bg-amber-400/15 py-2.5 text-amber-400 hover:bg-amber-400/25 transition-colors"
-            title="New Session"
-          >
-            <Plus size={20} strokeWidth={2} />
-            <span className="mt-1 text-[0.5625rem] font-sans font-semibold">New</span>
-          </Link>
-        </div>
-
         {/* Nav items */}
         <div className="flex flex-col items-center w-full px-1 space-y-1.5">
           {railGroups.map((item, i) => renderRailItem(item, `rail-${i}`))}