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/search.go

@@ -0,0 +1,136 @@
+package handler
+
+import (
+	"context"
+	"fmt"
+	"strconv"
+	"strings"
+
+	"github.com/go-telegram/bot/models"
+
+	"uptodownBot/internal/domain"
+)
+
+func (h *Handler) handleSearchCommand(ctx context.Context, msg *models.Message, userID int64) {
+	h.promptForInput(ctx, msg.Chat.ID, 0, userID, PendingSearch,
+		"Enter a YouTube search query:", map[string]string{"source": "youtube"})
+}
+
+func (h *Handler) handleMusicSearchCommand(ctx context.Context, msg *models.Message, userID int64) {
+	h.promptForInput(ctx, msg.Chat.ID, 0, userID, PendingSearch,
+		"Enter a YouTube Music search query:", map[string]string{"source": "ytmusic"})
+}
+
+func (h *Handler) handleSearchQuery(ctx context.Context, chatID int64, text string, userID int64, source string) {
+	results, err := h.YtDlp.Search(text, source, 10)
+	if err != nil {
+		h.sendText(ctx, chatID, fmt.Sprintf("Search failed: %s", err.Error()))
+		return
+	}
+	if len(results) == 0 {
+		h.sendText(ctx, chatID, "No results found.")
+		return
+	}
+
+	state := &domain.SearchState{
+		Query:   text,
+		Entries: results,
+		Page:    0,
+		PerPage: 5,
+		Source:  source,
+	}
+	ss := &stepState{SearchState: state}
+	h.setUserStepState(chatID, ss)
+
+	kb := searchResultsKeyboard(state)
+	h.sendWithKB(ctx, chatID, fmt.Sprintf("Search results for '%s':", text), kb)
+}
+
+func (h *Handler) handleSearchCallback(ctx context.Context, chatID int64, msgID int, userID int64, data string) {
+	switch {
+	case data == "refresh":
+		ss := h.getUserStepState(chatID)
+		if ss == nil || ss.SearchState == nil {
+			return
+		}
+		h.handleSearchQuery(ctx, chatID, ss.SearchState.Query, userID, ss.SearchState.Source)
+	case strings.HasPrefix(data, "page_"):
+		h.handleSearchPage(ctx, chatID, msgID, userID, data[5:])
+	case strings.HasPrefix(data, "select_"):
+		h.handleSearchSelect(ctx, chatID, msgID, userID, data[7:])
+	}
+}
+
+func (h *Handler) handleSearchPage(ctx context.Context, chatID int64, msgID int, userID int64, pageStr string) {
+	ss := h.getUserStepState(chatID)
+	if ss == nil || ss.SearchState == nil {
+		return
+	}
+	page, err := strconv.Atoi(pageStr)
+	if err != nil {
+		return
+	}
+	totalPages := (len(ss.SearchState.Entries) + ss.SearchState.PerPage - 1) / ss.SearchState.PerPage
+	if page < 0 || page >= totalPages {
+		return
+	}
+	ss.SearchState.Page = page
+	h.setUserStepState(chatID, ss)
+
+	kb := searchResultsKeyboard(ss.SearchState)
+	h.editText(ctx, chatID, msgID, fmt.Sprintf("Search results for '%s':", ss.SearchState.Query), &kb)
+}
+
+func (h *Handler) handleSearchSelect(ctx context.Context, chatID int64, msgID int, userID int64, entryURL string) {
+	h.clearStepState(chatID)
+	h.editText(ctx, chatID, msgID, "Fetching media info...", nil)
+	h.handleURLInput(ctx, chatID, entryURL, userID)
+}
+
+func searchResultsKeyboard(state *domain.SearchState) models.InlineKeyboardMarkup {
+	totalPages := (len(state.Entries) + state.PerPage - 1) / state.PerPage
+	if totalPages < 1 {
+		totalPages = 1
+	}
+
+	rows := [][]models.InlineKeyboardButton{}
+	start := state.Page * state.PerPage
+	end := start + state.PerPage
+	if end > len(state.Entries) {
+		end = len(state.Entries)
+	}
+
+	for i := start; i < end; i++ {
+		e := state.Entries[i]
+		title := e.Title
+		if len(title) > 40 {
+			title = title[:37] + "..."
+		}
+		label := title
+		if e.Duration > 0 {
+			label += fmt.Sprintf(" (%s)", formatDuration(e.Duration))
+		}
+		rows = append(rows, []models.InlineKeyboardButton{
+			{Text: label, CallbackData: "search_select_" + e.URL},
+		})
+	}
+
+	navRow := []models.InlineKeyboardButton{}
+	navRow = append(navRow, models.InlineKeyboardButton{
+		Text: "<", CallbackData: fmt.Sprintf("search_page_%d", state.Page-1),
+	})
+	navRow = append(navRow, models.InlineKeyboardButton{
+		Text: fmt.Sprintf("Page %d/%d", state.Page+1, totalPages), CallbackData: "noop",
+	})
+	navRow = append(navRow, models.InlineKeyboardButton{
+		Text: ">", CallbackData: fmt.Sprintf("search_page_%d", state.Page+1),
+	})
+	rows = append(rows, navRow)
+
+	rows = append(rows, []models.InlineKeyboardButton{
+		{Text: "New Search", CallbackData: "search_refresh"},
+		{Text: "Cancel", CallbackData: "cancel_dl"},
+	})
+
+	return models.InlineKeyboardMarkup{InlineKeyboard: rows}
+}