feat: Implement sorting of peers by latest message timestamp and unread status in Nostr chat

- Introduce a computed property to sort peers based on the latest message timestamp and unread message count, enhancing the user experience by prioritizing relevant conversations.
- Add methods to track and retrieve the latest message timestamp for each peer, ensuring accurate sorting.
- Update the ChatComponent to utilize the new sorting logic, improving the display of peers in the chat interface.

refactor: Reorganize fuzzy search and mobile detection logic in ChatComponent

- Move fuzzy search implementation and mobile detection methods to improve code clarity and maintainability.
- Ensure consistent functionality for searching peers by username or pubkey with typo tolerance.
- Maintain mobile navigation logic for better user experience on smaller devices.

src/components/nostr/ChatComponent.vue

@@ -401,6 +401,62 @@ const scrollTarget = ref<HTMLElement | null>(null)
 // Mobile detection
 const isMobile = ref(false)
 
+// Nostr chat composable
+const {
+  isConnected,
+  messages,
+  connect,
+  disconnect,
+  subscribeToPeer,
+  subscribeToPeerForNotifications,
+  sendMessage: sendNostrMessage,
+  onMessageAdded,
+  markMessagesAsRead,
+  getUnreadCount,
+  getTotalUnreadCount,
+  getLatestMessageTimestamp
+} = useNostrChat()
+
+// Computed
+const currentMessages = computed(() => {
+  if (!selectedPeer.value) return []
+  return messages.value.get(selectedPeer.value.pubkey) || []
+})
+
+// Sort peers by latest message timestamp (newest first) and unread status
+const sortedPeers = computed(() => {
+  const sorted = [...peers.value].sort((a, b) => {
+    const aTimestamp = getLatestMessageTimestamp(a.pubkey)
+    const bTimestamp = getLatestMessageTimestamp(b.pubkey)
+    const aUnreadCount = getUnreadCount(a.pubkey)
+    const bUnreadCount = getUnreadCount(b.pubkey)
+    
+    // First, sort by unread count (peers with unread messages appear first)
+    if (aUnreadCount > 0 && bUnreadCount === 0) return -1
+    if (aUnreadCount === 0 && bUnreadCount > 0) return 1
+    
+    // Then, sort by latest message timestamp (newest first)
+    if (aTimestamp !== bTimestamp) {
+      return bTimestamp - aTimestamp
+    }
+    
+    // Finally, sort alphabetically by username for peers with same timestamp
+    return (a.username || '').localeCompare(b.username || '')
+  })
+  
+  // Debug logging (only in development)
+  if (process.env.NODE_ENV === 'development' && sorted.length > 0) {
+    console.log('Sorted peers:', sorted.map(p => ({
+      username: p.username,
+      pubkey: p.pubkey.slice(0, 8) + '...',
+      latestTimestamp: getLatestMessageTimestamp(p.pubkey),
+      unreadCount: getUnreadCount(p.pubkey)
+    })))
+  }
+  
+  return sorted
+})
+
 // Fuzzy search for peers
 // This integrates the useFuzzySearch composable to provide intelligent search functionality
 // for finding peers by username or pubkey with typo tolerance and scoring
@@ -410,7 +466,7 @@ const {
   isSearching,
   resultCount,
   clearSearch
-} = useFuzzySearch(peers, {
+} = useFuzzySearch(sortedPeers, {
   fuseOptions: {
     keys: [
       { name: 'username', weight: 0.7 },  // Username has higher weight for better UX
@@ -442,27 +498,6 @@ const goBackToPeers = () => {
   selectedPeer.value = null
 }
 
-// Nostr chat composable
-const {
-  isConnected,
-  messages,
-  connect,
-  disconnect,
-  subscribeToPeer,
-  subscribeToPeerForNotifications,
-  sendMessage: sendNostrMessage,
-  onMessageAdded,
-  markMessagesAsRead,
-  getUnreadCount,
-  getTotalUnreadCount
-} = useNostrChat()
-
-// Computed
-const currentMessages = computed(() => {
-  if (!selectedPeer.value) return []
-  return messages.value.get(selectedPeer.value.pubkey) || []
-})
-
 // Methods
 const loadPeers = async () => {
   try {