feat(web): add browser web client with IndexedDB, Service Worker, and PWA

Create sdks/web/ with a vanilla TypeScript web client:
- IndexedDB local store for conversations, messages, and identity
- WebSocket transport connecting to the server bridge
- Service Worker with cache-first strategy for offline support
- PWA manifest for installable web app
- Dark-themed responsive UI with sidebar, messages, and input bar
- Connection status badge and MLS epoch indicator in header
- Unread message count badges on conversations

sdks/web/public/sw.js

@@ -0,0 +1,96 @@
+/**
+ * quicproquo Service Worker — provides offline caching and background
+ * notification support for the PWA.
+ */
+
+const CACHE_NAME = "qpq-cache-v1";
+const STATIC_ASSETS = [
+  "/",
+  "/index.html",
+  "/style.css",
+  "/app.js",
+  "/manifest.json",
+];
+
+// Install: cache static assets.
+self.addEventListener("install", (event) => {
+  event.waitUntil(
+    caches.open(CACHE_NAME).then((cache) => cache.addAll(STATIC_ASSETS)),
+  );
+  self.skipWaiting();
+});
+
+// Activate: clean up old caches.
+self.addEventListener("activate", (event) => {
+  event.waitUntil(
+    caches.keys().then((keys) =>
+      Promise.all(
+        keys
+          .filter((key) => key !== CACHE_NAME)
+          .map((key) => caches.delete(key)),
+      ),
+    ),
+  );
+  self.clients.claim();
+});
+
+// Fetch: serve from cache, fall back to network.
+self.addEventListener("fetch", (event) => {
+  // Only cache GET requests for same-origin resources.
+  if (event.request.method !== "GET") return;
+
+  event.respondWith(
+    caches.match(event.request).then((cached) => {
+      if (cached) return cached;
+      return fetch(event.request).then((response) => {
+        // Cache successful same-origin responses.
+        if (
+          response.ok &&
+          new URL(event.request.url).origin === self.location.origin
+        ) {
+          const clone = response.clone();
+          caches.open(CACHE_NAME).then((cache) => {
+            cache.put(event.request, clone);
+          });
+        }
+        return response;
+      });
+    }),
+  );
+});
+
+// Push notifications (future: wired to server push events).
+self.addEventListener("push", (event) => {
+  if (!event.data) return;
+
+  let payload;
+  try {
+    payload = event.data.json();
+  } catch {
+    payload = { title: "quicproquo", body: event.data.text() };
+  }
+
+  event.waitUntil(
+    self.registration.showNotification(payload.title || "quicproquo", {
+      body: payload.body || "New message",
+      icon: "/icon-192.png",
+      badge: "/icon-192.png",
+      tag: payload.conversationId || "default",
+    }),
+  );
+});
+
+// Notification click: open the app.
+self.addEventListener("notificationclick", (event) => {
+  event.notification.close();
+  event.waitUntil(
+    self.clients
+      .matchAll({ type: "window" })
+      .then((clients) => {
+        if (clients.length > 0) {
+          return clients[0].focus();
+        }
+        return self.clients.openWindow("/");
+      }),
+  );
+});