feat(queue): server-side PTY-inject + idle-drained follow-up queue (W2)

The walk-away primitive: queue follow-up prompts and let a session advance itself
while you're gone — "run the tests" drains, and when Claude next goes idle "open a
PR" drains. Injection reuses writeInput (byte-identical to a keystroke, broadcasts
to all mirrored devices); the byte-shuttle is untouched.

- POST/GET/DELETE /live-sessions/:id/queue — POST/DELETE behind requireAllowedOrigin
  + a per-IP rate limit (QUEUE_RATE_MAX=20/min) + SESSION_ID_RE; text non-empty,
  byte-capped (QUEUE_ITEM_MAX_BYTES=4096, 16kb body), count-capped (QUEUE_MAX_ITEMS=10).
- Bounded per-session queue in manager (enqueueFollowup/drainOne/clearQueue);
  new optional queueLength on LiveSessionInfo.
- Idle drain: the Stop/SessionEnd /hook branch scheduleDrain()s a debounced timer
  (QUEUE_SETTLE_MS=1500). It drains exactly one entry only if the session still
  exists, hasn't exited, produced no output during settle, and is idle — three
  guards (debounced single timer + pop-one + settle re-check) → one entry per idle.
- New additive ServerMessage {type:'queue',length} broadcasts the count to mirrors
  (⧗N badge); FE enqueue via the quick-reply editor + TabApp.enqueueToActive.

Injected bytes go verbatim to the PTY (never built into a shell command). Verified
independently: typecheck + build:web clean, 1737 tests pass (real-PTY integration
covers idle-drain / one-per-idle / settle-guard). Foundation for templated launches,
auto-continue, and issue-intake (docs/ROADMAP.md).

public/quick-reply.ts

@@ -147,6 +147,10 @@ function clearChildren(parent: HTMLElement): void {
 export interface QuickReplyOpts {
   /** Called with the full byte string to inject into the terminal. */
   onSend: (data: string) => void
+  /** W2: optional. When provided, the snippet editor gains a "Queue" button that
+   *  enqueues the typed text as a follow-up prompt (fired on next idle) instead of
+   *  sending it now. `appendEnter` mirrors the editor checkbox. */
+  onQueue?: (text: string, appendEnter: boolean) => void
 }
 
 /** Returned by mountQuickReply to allow cleanup. */
@@ -165,7 +169,7 @@ export interface QuickReplyHandle {
  * Labels are set via textContent — never innerHTML (SEC-L3).
  */
 export function mountQuickReply(container: HTMLElement, opts: QuickReplyOpts): QuickReplyHandle {
-  const { onSend } = opts
+  const { onSend, onQueue } = opts
   // Track disposers for all event listeners so dispose() is clean.
   const disposers: Array<() => void> = []
 
@@ -233,6 +237,22 @@ export function mountQuickReply(container: HTMLElement, opts: QuickReplyOpts): Q
     editor.appendChild(labelInput)
     editor.appendChild(enterWrap)
     editor.appendChild(saveBtn)
+
+    // W2: "Queue" defers the typed text as a follow-up prompt (fires on next
+    // idle) rather than saving it as a chip. Shown only when a handler is wired.
+    if (onQueue !== undefined) {
+      const queueBtn = el('button', 'qr-editor-queue', 'Queue')
+      queueBtn.title = 'Queue as a follow-up (runs when Claude next goes idle)'
+      function onQueueClick() {
+        const text = textInput.value.trim()
+        if (!text) return // empty text — no-op, editor stays open
+        onQueue?.(text, enterCheck.checked)
+        editor.remove()
+      }
+      queueBtn.addEventListener('click', onQueueClick)
+      editor.appendChild(queueBtn)
+    }
+
     editor.appendChild(cancelBtn)
 
     container.appendChild(editor)