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/urlState.ts

@@ -91,6 +91,7 @@ export const PAGES = [
   "config",
   "users",
   "notifications",
+  "messages",
 ] as const;
 
 export type Page = (typeof PAGES)[number];