feat(chat): unread count + sidebar badge (Q1)

Track a per-conversation "last seen" watermark (message timestamp) on App:
- chatUnreadCount() sums incoming messages newer than each conversation's
  watermark; surfaced as SidebarStatus.chatUnreadCount → a badge on the Chat nav
  item (mirrors the History/Peers badges).
- Viewing a thread marks it seen (markChatConversationSeen while displayed).
- Baseline on load: existing stored messages are marked seen, so only messages
  that arrive while the app is open badge as unread.
- Wiped in resetChatSession so unread state never leaks across a wallet switch.
In-memory only (resets on app restart); persistence is a later refinement.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/ui/sidebar.h

@@ -149,6 +149,7 @@ struct SidebarStatus {
     int  unconfirmedTxCount = 0;   // badge on History
     bool miningActive       = false; // green dot on Mining
     int  peerCount          = 0;   // badge on Peers
+    int  chatUnreadCount    = 0;   // badge on Chat (unread incoming messages)
     // Exit
     bool exitClicked        = false;
     // Branding logo (optional — loaded at startup)
@@ -715,6 +716,8 @@ inline bool RenderSidebar(NavPage& current, float sidebarWidth, float contentHei
                 dotOnly = true; badgeCol = Success();
             } else if (item.page == NavPage::Peers && status.peerCount > 0) {
                 badgeCount = status.peerCount;
+            } else if (item.page == NavPage::Chat && status.chatUnreadCount > 0) {
+                badgeCount = status.chatUnreadCount;
             }
 
             if (badgeCount > 0 || dotOnly) {