feat: content header with collapse toggle + realtime indicator

- New SidebarProvider context for shared collapse state
- ContentHeader visible on desktop: collapse icon left, "Live" right
- Collapse button removed from sidebar bottom (moved to header)
- Keyboard shortcut [ handled by context, not sidebar
- Realtime indicator polls every 5s, ticks every 1s for freshness

lib/sidebar-context.tsx

@@ -0,0 +1,68 @@
+'use client'
+
+import { createContext, useContext, useState, useCallback, useEffect } from 'react'
+
+const SIDEBAR_KEY = 'pulse_sidebar_collapsed'
+
+interface SidebarState {
+  collapsed: boolean
+  toggle: () => void
+  expand: () => void
+  collapse: () => void
+}
+
+const SidebarContext = createContext<SidebarState>({
+  collapsed: true,
+  toggle: () => {},
+  expand: () => {},
+  collapse: () => {},
+})
+
+export function SidebarProvider({ children }: { children: React.ReactNode }) {
+  const [collapsed, setCollapsed] = useState(() => {
+    if (typeof window === 'undefined') return true
+    return localStorage.getItem(SIDEBAR_KEY) !== 'false'
+  })
+
+  const toggle = useCallback(() => {
+    setCollapsed((prev) => {
+      const next = !prev
+      localStorage.setItem(SIDEBAR_KEY, String(next))
+      return next
+    })
+  }, [])
+
+  const expand = useCallback(() => {
+    setCollapsed(false)
+    localStorage.setItem(SIDEBAR_KEY, 'false')
+  }, [])
+
+  const collapse = useCallback(() => {
+    setCollapsed(true)
+    localStorage.setItem(SIDEBAR_KEY, 'true')
+  }, [])
+
+  // Keyboard shortcut: [ to toggle
+  useEffect(() => {
+    const handler = (e: KeyboardEvent) => {
+      const tag = (e.target as HTMLElement)?.tagName
+      if (tag === 'INPUT' || tag === 'TEXTAREA' || tag === 'SELECT') return
+      if (e.key === '[' && !e.metaKey && !e.ctrlKey && !e.altKey) {
+        e.preventDefault()
+        toggle()
+      }
+    }
+    document.addEventListener('keydown', handler)
+    return () => document.removeEventListener('keydown', handler)
+  }, [toggle])
+
+  return (
+    <SidebarContext.Provider value={{ collapsed, toggle, expand, collapse }}>
+      {children}
+    </SidebarContext.Provider>
+  )
+}
+
+export function useSidebar() {
+  return useContext(SidebarContext)
+}