feat(aiui): receive a Cmd+K handoff and prefill the composer

Completes the 'Talk to AIUI about it' path from the other side. archyBridge
gains a chat:prefill case behind its existing parent-origin validation, and
ChatInput prefills + focuses with the caret at the end.

Prefills rather than auto-sends: the operator sees and can amend the question
before it costs a model call, and a draft they had already started is never
clobbered by a background handoff. Auto-send is the natural seam for the
follow-up that actions things directly.

The bridge buffers a prefill that arrives before the composer mounts (collapsed
chat, mobile content tab) and replays it on registration, so a Cmd+K ask into a
cold frame is not silently dropped. onPrefill returns an unsubscribe so a
remounting composer cannot leak a stale handler.

Verified: vue-tsc clean; AIUI suite 332 passed. The 3 remaining failures
(seed-songs extraction x2, web-search system prompt) are pre-existing — I
confirmed by reverting 13-01's two AIUI files to their parent state and
reproducing the identical 3 failures without any phase-13 change present.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

aiui/packages/app/src/services/archyBridge.ts

@@ -101,6 +101,19 @@ function handleMessage(event: MessageEvent) {
       }
       break
     }
+
+    // Archy's ⌘K search offers "Talk to AIUI about it"; this carries the text
+    // the operator typed there into our composer.
+    case 'chat:prefill': {
+      const text = typeof msg.text === 'string' ? msg.text : ''
+      if (!text) break
+      if (prefillCallback) prefillCallback(text)
+      // Buffer when nothing is listening yet: the composer may not be mounted
+      // at handshake time (collapsed chat, mobile content tab), and dropping
+      // the text would silently lose what the operator typed.
+      else bufferedPrefill = text
+      break
+    }
   }
 }
 
@@ -116,6 +129,9 @@ function handleMessage(event: MessageEvent) {
  * dev server port). `document.referrer` is the standard, cross-origin-safe
  * way an iframed document learns its embedding parent's URL.
  */
+let prefillCallback: ((text: string) => void) | null = null
+let bufferedPrefill = ''
+
 function deriveParentOrigin(): string {
   if (typeof document !== 'undefined' && document.referrer) {
     try {
@@ -142,6 +158,23 @@ export const archyBridge = {
     postToParent({ type: 'ready' })
   },
 
+  /**
+   * Register the composer's prefill handler. Replays a prefill that arrived
+   * before the composer mounted, so a ⌘K ask is never dropped on a cold frame.
+   * Returns an unsubscribe so a remounting composer does not leak the old one.
+   */
+  onPrefill(fn: (text: string) => void) {
+    prefillCallback = fn
+    if (bufferedPrefill) {
+      const text = bufferedPrefill
+      bufferedPrefill = ''
+      fn(text)
+    }
+    return () => {
+      if (prefillCallback === fn) prefillCallback = null
+    }
+  },
+
   /** Clean up listeners */
   destroy() {
     window.removeEventListener('message', handleMessage)