email: push new-mail to /email via SSE (IMAP IDLE -> sidecar -> server -> EventSource)

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/server.tsx

@@ -15,6 +15,7 @@ import { findEntryByProxyId, touchEntry } from './servers/api/dev-server/router'
 import officerWeb from './apps/officer-web/index.html';
 import { startBrowserRelay } from './servers/api/browser/relay';
 import { registerSidecar, unregisterSidecar, handleSidecarMessage } from './servers/sidecar-registry';
+import { broadcastEmailNew } from './servers/api/email/email';
 import type { SidecarRegistration } from './servers/sidecar/registration-protocol';
 import { toShellUsername } from './servers/data-path';
 
@@ -71,6 +72,12 @@ const sidecarWebsocket = {
         return;
       }
 
+      // Email IDLE watcher reporting new mail → push to that user's /email SSE clients.
+      if (msg.type === 'email:new' && typeof msg.userEmail === 'string') {
+        broadcastEmailNew(msg.userEmail);
+        return;
+      }
+
       const id = sidecarConnections.get(ws);
       if (id) {
         handleSidecarMessage(id, msg);