feat(demo): P3.5 inbox sidebar + inbox smoke (P3 complete)

message-demo gains a per-person Inbox rail (useInbox, done/snooze); sending
surfaces a NEEDS_REPLY item in the other pane; reading auto-resolves it.
smoke-inbox.mjs proves the event-driven flow end-to-end (send -> relay ->
projector -> inbox -> read -> DONE). Realtime smoke still passes.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

apps/message-demo/src/App.tsx

@@ -1,5 +1,6 @@
 import { useEffect, useState } from 'react';
 import { MessageProvider, useThread, useMessages } from '@insignia/iios-message-web';
+import { InboxProvider, useInbox } from '@insignia/iios-inbox-web';
 
 const SERVICE = 'http://localhost:3200';
 const APP_ID = 'portal-demo';
@@ -83,12 +84,35 @@ function ChatInner({
   );
 }
 
+function InboxSidebar() {
+  const { items, done, snooze } = useInbox({ state: 'OPEN' });
+  return (
+    <div style={{ width: 170, borderRight: '1px solid #ddd', padding: 8, fontSize: 12, fontFamily: 'sans-serif' }}>
+      <b>Inbox ({items.length})</b>
+      {items.length === 0 && <div style={{ color: '#999', marginTop: 6 }}>nothing to reply to</div>}
+      {items.map((i) => (
+        <div key={i.id} style={{ padding: '6px 0', borderBottom: '1px solid #eee' }}>
+          <div style={{ fontWeight: 600 }}>{i.title}</div>
+          <div style={{ color: '#999' }}>{i.kind}</div>
+          <button style={{ marginRight: 4 }} onClick={() => void done(i.id)}>done</button>
+          <button onClick={() => void snooze(i.id)}>snooze</button>
+        </div>
+      ))}
+    </div>
+  );
+}
+
 function Pane(props: { token: string | null; label: string; threadId: string | null; onCreated?: (id: string) => void }) {
   if (!props.token) return <div style={{ flex: 1, margin: 8 }}>loading {props.label}…</div>;
   return (
-    <MessageProvider serviceUrl={SERVICE} token={props.token}>
-      <ChatInner label={props.label} threadId={props.threadId} onCreated={props.onCreated} />
-    </MessageProvider>
+    <div style={{ flex: 1, display: 'flex', margin: 8, border: '1px solid #ccc', borderRadius: 8, overflow: 'hidden' }}>
+      <InboxProvider serviceUrl={SERVICE} token={props.token}>
+        <InboxSidebar />
+      </InboxProvider>
+      <MessageProvider serviceUrl={SERVICE} token={props.token}>
+        <ChatInner label={props.label} threadId={props.threadId} onCreated={props.onCreated} />
+      </MessageProvider>
+    </div>
   );
 }