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/chatDock.ts

@@ -0,0 +1,56 @@
+// App-wide store of open floating chat windows (the Messenger-style dock, bottom-right).
+// A window can be opened from anywhere (e.g. a conversation's "pop out" button) and stays
+// open across page navigation. Plain external store so any component can read/drive it.
+import { useSyncExternalStore } from "react";
+
+export interface DockChat {
+  partnerId: number;
+  name: string;
+  avatar: string | null;
+  minimized: boolean;
+}
+
+const MAX_OPEN = 3; // keep the dock from overflowing the corner
+let chats: DockChat[] = [];
+const subs = new Set<() => void>();
+
+function emit(next: DockChat[]): void {
+  chats = next;
+  for (const s of subs) s();
+}
+
+export function openChat(partner: { id: number; name: string; avatar_url: string | null }): void {
+  const existing = chats.find((c) => c.partnerId === partner.id);
+  if (existing) {
+    // Re-opening focuses it: ensure expanded and move to the front.
+    emit([
+      { ...existing, minimized: false },
+      ...chats.filter((c) => c.partnerId !== partner.id),
+    ]);
+    return;
+  }
+  const next = [
+    { partnerId: partner.id, name: partner.name, avatar: partner.avatar_url, minimized: false },
+    ...chats,
+  ].slice(0, MAX_OPEN);
+  emit(next);
+}
+
+export function closeChat(partnerId: number): void {
+  emit(chats.filter((c) => c.partnerId !== partnerId));
+}
+
+export function toggleMinimize(partnerId: number): void {
+  emit(chats.map((c) => (c.partnerId === partnerId ? { ...c, minimized: !c.minimized } : c)));
+}
+
+export function useDockChats(): DockChat[] {
+  return useSyncExternalStore(
+    (cb) => {
+      subs.add(cb);
+      return () => subs.delete(cb);
+    },
+    () => chats,
+    () => chats
+  );
+}