feat(messages): standalone Messages module + floating chat dock

Move messaging out of the notification center into its own left-nav module
(own page, own unread badge), so a reload returns to it and notifications stay
separate. Add a Messenger-style floating dock (bottom-right): pop a conversation
out from the page, keep chatting across navigation, minimise (rollup) or close.

- Messages is now a routed page; NotificationsPanel reverts to inbox-only and the
  nav badge no longer mixes in messages.
- Extract shared KeyGate + ChatThread (used by both the page and dock windows);
  e2ee exposes a shared unlock subscription so page and dock agree.
- ChatDock (always mounted for human users) owns the app-wide live-message
  subscription and per-device key restore. EN/HU/DE strings.

frontend/src/lib/messaging.ts

@@ -0,0 +1,21 @@
+// Shared messaging helpers used by both the Messages page and the floating chat dock.
+import { useSyncExternalStore } from "react";
+import { api } from "./api";
+import { isUnlocked, subscribeUnlock } from "./e2ee";
+
+export const SYSTEM_ID = 0; // synthetic "Siftlode" system conversation partner id
+
+// Set-once cache of partner public keys (the server is the directory; keys never change).
+const pubCache = new Map<number, string>();
+export async function partnerPub(partnerId: number): Promise<string> {
+  const cached = pubCache.get(partnerId);
+  if (cached) return cached;
+  const r = await api.messagePublicKey(partnerId);
+  pubCache.set(partnerId, r.public_key);
+  return r.public_key;
+}
+
+// Live "is secure messaging unlocked on this device" — shared so the page and the dock agree.
+export function useUnlocked(): boolean {
+  return useSyncExternalStore(subscribeUnlock, isUnlocked, isUnlocked);
+}