frontend: messages visual polish

Same layout, better inbox: avatars on conversation rows, a numeric unread
badge (kept live by the socket handler), primary-tinted timestamps for unread
rows and softer hover states. In the thread: day separators
(Today/Yesterday/date), consecutive same-sender messages within 5 minutes
grouped with one sender label + one timestamp and tightened corners, and a
"Start a conversation" button on the empty state.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

frontend/lib/messages.ts

@@ -22,6 +22,8 @@ export type ConversationSummary = {
   participants: Participant[];
   lastMessage: ConversationMessage | null;
   unread: boolean;
+  // Messages from others newer than the caller's read pointer.
+  unreadCount: number;
   updatedAt: string;
 };