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/domain/types.go

@@ -177,3 +177,12 @@ type PlaylistState struct {
 	PerPage  int
 	Selected map[string]bool
 }
+
+// SearchState tracks the user's current search results flow.
+type SearchState struct {
+	Query   string
+	Entries []PlaylistEntry
+	Page    int
+	PerPage int
+	Source  string // "youtube" or "ytmusic"
+}