feat: add in-memory media info cache and YouTube search feature

- Add in-memory LRU cache (200 entries, 30 min TTL) to yt-dlp Client for
  GetMediaInfo and GetPlaylistInfo results, avoiding redundant yt-dlp calls
  for the same URL within a session
- Add YouTube (/search) and YouTube Music (/music) search with paginated
  results (5 per page), user selects a result to start the download flow
- Add SearchState type, new search.go handler, search results keyboard with
  < > navigation and New Search button
- Add Search button to main menu keyboard
- Update help text with new commands

internal/handler/handler.go

@@ -23,8 +23,9 @@ import (
 type PendingKind string
 
 const (
-	PendingURL PendingKind = "url"
-	PendingDRM PendingKind = "drm"
+	PendingURL    PendingKind = "url"
+	PendingDRM    PendingKind = "drm"
+	PendingSearch PendingKind = "search"
 )
 
 type PendingInput struct {
@@ -185,6 +186,10 @@ func (h *Handler) routeCommand(ctx context.Context, msg *models.Message, userID
 		h.handleHistory(ctx, msg, userID)
 	case "/download":
 		h.handleDownloadCommand(ctx, msg, userID)
+	case "/search":
+		h.handleSearchCommand(ctx, msg, userID)
+	case "/music":
+		h.handleMusicSearchCommand(ctx, msg, userID)
 	default:
 		h.sendText(ctx, msg.Chat.ID, "Unknown command")
 	}
@@ -226,6 +231,9 @@ func (h *Handler) HandleCallback(ctx context.Context, cb *models.CallbackQuery)
 	case data == "download":
 		h.handleDownloadPrompt(ctx, chatID, msgID, cb.ID, userID)
 		h.answerCb(ctx, cb.ID)
+	case data == "search":
+		h.promptForInput(ctx, chatID, msgID, userID, PendingSearch, "Enter a YouTube search query:", map[string]string{"source": "youtube"})
+		h.answerCb(ctx, cb.ID)
 	case data == "settings":
 		h.settingsCallback(ctx, chatID, msgID, cb.ID, userID)
 	case data == "help":
@@ -280,6 +288,8 @@ func (h *Handler) routePrefixedCallback(ctx context.Context, chatID int64, msgID
 		h.handleSettingsSet(ctx, chatID, msgID, userID, data[13:])
 	case strings.HasPrefix(data, "settings_"):
 		h.handleSettingsSelection(ctx, chatID, msgID, userID, data[9:])
+	case strings.HasPrefix(data, "search_"):
+		h.handleSearchCallback(ctx, chatID, msgID, userID, data[7:])
 	}
 }
 
@@ -302,6 +312,12 @@ func (h *Handler) processPendingInput(ctx context.Context, msg *models.Message,
 		h.handleURLInput(ctx, msg.Chat.ID, text, userID)
 	case PendingDRM:
 		h.handleDRMSearch(ctx, msg.Chat.ID, text, userID)
+	case PendingSearch:
+		source := "youtube"
+		if pi.Data != nil && pi.Data["source"] != "" {
+			source = pi.Data["source"]
+		}
+		h.handleSearchQuery(ctx, msg.Chat.ID, text, userID, source)
 	default:
 		h.sendText(ctx, msg.Chat.ID, "Unknown input type")
 	}
@@ -457,6 +473,8 @@ func (h *Handler) handleHelp(ctx context.Context, msg *models.Message) {
 /settings - Open settings
 /help - Show this help
 /history - View download history
+/search - Search YouTube
+/music - Search YouTube Music
 
 Just send me a URL to start downloading.`
 	h.sendText(ctx, msg.Chat.ID, text)