feat(v0.3): H4 — live Claude status badge + notifications + setup-hooks

- terminal-session: handle 'status' frame → claudeStatus + onClaudeStatus
- tabs: per-tab Claude glyph (⚙ working / ⏳ waiting / ✓ idle); inactive
  'waiting' tab gets an amber highlight + a browser notification (permission
  requested on first tab switch)
- scripts/setup-hooks.mjs + 'npm run setup-hooks': idempotently install/remove
  command hooks in ~/.claude/settings.json (inline curl to $WEBTERM_HOOK_URL with
  $WEBTERM_SESSION; no-op outside web-terminal); backs up settings.json
- Browser-verified end-to-end: PermissionRequest→⏳, PreToolUse→⚙, Stop→✓;
  inactive waiting tab shows amber + glyph. 205 tests green.

public/style.css

@@ -202,6 +202,18 @@ html, body {
   font-weight: 600;
 }
 
+/* Claude Code activity glyph (H2/H4) */
+.tab-claude {
+  margin-right: 6px;
+  font-size: 12px;
+  flex: none;
+}
+/* A background tab that needs approval gets an amber outline. */
+.tab.claude-waiting {
+  background-color: #3a2a10;
+  box-shadow: inset 0 -2px 0 #d29922;
+}
+
 /* Drag-to-reorder feedback. */
 .tab.dragging {
   opacity: 0.4;

public/tabs.ts

@@ -40,6 +40,7 @@ export class TabApp {
   private activeIndex = -1
   private editingIndex = -1
   private dragIndex = -1
+  private notifyAsked = false
   private readonly paneHost: HTMLElement
   private readonly tabBar: HTMLElement
 
@@ -135,6 +136,13 @@ export class TabApp {
         this.refreshTab(entry)
       },
       onStatus: () => this.refreshTab(entry),
+      onClaudeStatus: (status) => {
+        this.refreshTab(entry)
+        // Notify when a background tab needs approval (H2/H4).
+        if (status === 'waiting' && this.tabs.indexOf(entry) !== this.activeIndex) {
+          this.notify(entry)
+        }
+      },
     })
     this.paneHost.appendChild(entry.session.el)
     this.tabs.push(entry)
@@ -151,6 +159,7 @@ export class TabApp {
 
   activate(i: number): void {
     if (i < 0 || i >= this.tabs.length) return
+    this.maybeAskNotify() // first switch is a user gesture — request notif permission
     this.activeIndex = i
     const entry = this.tabs[i]
     if (entry) entry.hasActivity = false // viewing clears the unread dot
@@ -218,6 +227,22 @@ export class TabApp {
     this.tabs[this.activeIndex]?.session.clearSearch()
   }
 
+  /** Ask for notification permission once, on a user gesture (H2/H4). */
+  private maybeAskNotify(): void {
+    if (this.notifyAsked) return
+    this.notifyAsked = true
+    if (typeof Notification !== 'undefined' && Notification.permission === 'default') {
+      void Notification.requestPermission()
+    }
+  }
+
+  /** Browser notification for a background tab needing approval. */
+  private notify(entry: TabEntry): void {
+    if (typeof Notification === 'undefined' || Notification.permission !== 'granted') return
+    const title = this.displayTitle(entry, this.tabs.indexOf(entry))
+    new Notification(`Claude needs you — ${title}`, { body: 'Waiting for approval' })
+  }
+
   /* ── rendering ───────────────────────────────────────────────── */
 
   /** In-place update of one tab's classes/label/dot — never destroys the DOM. */
@@ -227,12 +252,19 @@ export class TabApp {
     const idx = this.tabs.indexOf(entry)
     el.classList.toggle('active', idx === this.activeIndex)
     el.classList.toggle('unread', entry.hasActivity && idx !== this.activeIndex)
+    const cs = entry.session.claudeStatus
+    el.classList.toggle('claude-waiting', cs === 'waiting' && idx !== this.activeIndex)
     const title = this.displayTitle(entry, idx)
     el.title = title
     const dot = el.querySelector('.tab-dot')
     if (dot) dot.className = `tab-dot dot-${entry.session.status}`
     const label = el.querySelector('.tab-label')
     if (label) label.textContent = title
+    const claude = el.querySelector('.tab-claude')
+    if (claude) {
+      claude.textContent =
+        cs === 'working' ? '⚙' : cs === 'waiting' ? '⏳' : cs === 'idle' ? '✓' : ''
+    }
   }
 
   /** Full rebuild — ONLY for structural changes (add/close/reorder/rename). */
@@ -311,6 +343,10 @@ export class TabApp {
         })
         tabEl.appendChild(label)
 
+        const claude = document.createElement('span')
+        claude.className = 'tab-claude'
+        tabEl.appendChild(claude)
+
         const close = document.createElement('button')
         close.className = 'tab-close'
         close.textContent = '×'

public/terminal-session.ts

@@ -12,7 +12,7 @@ import { Terminal } from '@xterm/xterm'
 import { FitAddon } from '@xterm/addon-fit'
 import { SearchAddon } from '@xterm/addon-search'
 import { WebLinksAddon } from '@xterm/addon-web-links'
-import type { ClientMessage, ServerMessage } from '../src/types.js'
+import type { ClaudeStatus, ClientMessage, ServerMessage } from '../src/types.js'
 import { folderFromTitle } from './title-util.js'
 
 const RESET = '\x1b[0m'
@@ -51,6 +51,8 @@ export interface TerminalSessionOpts {
   onTitle?: (title: string) => void
   /** Optional: fired when connection status changes (for the tab status dot). */
   onStatus?: (status: SessionStatus) => void
+  /** Optional: fired when Claude Code activity changes (from a hook, H2). */
+  onClaudeStatus?: (status: ClaudeStatus, detail?: string) => void
 }
 
 export class TerminalSession {
@@ -64,7 +66,9 @@ export class TerminalSession {
   private readonly onActivity: (() => void) | undefined
   private readonly onTitle: ((title: string) => void) | undefined
   private readonly onStatus: ((status: SessionStatus) => void) | undefined
+  private readonly onClaudeStatus: ((status: ClaudeStatus, detail?: string) => void) | undefined
   private statusValue: SessionStatus = 'connecting'
+  private claudeStatusValue: ClaudeStatus = 'unknown'
 
   private ws: WebSocket | null = null
   private sessionId: string | null
@@ -83,6 +87,7 @@ export class TerminalSession {
     this.onActivity = opts.onActivity
     this.onTitle = opts.onTitle
     this.onStatus = opts.onStatus
+    this.onClaudeStatus = opts.onClaudeStatus
 
     this.el = document.createElement('div')
     this.el.className = 'term-pane'
@@ -118,6 +123,11 @@ export class TerminalSession {
     return this.statusValue
   }
 
+  /** Current Claude Code activity (from hooks, H2). */
+  get claudeStatus(): ClaudeStatus {
+    return this.claudeStatusValue
+  }
+
   private setStatus(s: SessionStatus): void {
     this.statusValue = s
     this.onStatus?.(s)
@@ -206,6 +216,11 @@ export class TerminalSession {
         if (this.el.style.display === 'none') this.onActivity?.()
         break
       }
+      case 'status': {
+        this.claudeStatusValue = msg.status
+        this.onClaudeStatus?.(msg.status, msg.detail)
+        break
+      }
       case 'exit': {
         this.setStatus('exited')
         const reason = msg.reason ? ` (${msg.reason})` : ''