Add media browser integration for Home Assistant

- Implement async_browse_media() to enable browsing media folders through HA Media Browser UI
- Add async_play_media() to handle file playback from media browser
- Add play_media_file service for automation support
- Add BROWSE_MEDIA and PLAY_MEDIA feature flags
- Implement media browser API client methods (get_media_folders, browse_folder, play_media_file)
- Fix path separator handling for cross-platform compatibility

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

custom_components/remote_media_player/const.py

@@ -34,10 +34,15 @@ API_TOGGLE = "/api/media/toggle"
 API_SCRIPTS_LIST = "/api/scripts/list"
 API_SCRIPTS_EXECUTE = "/api/scripts/execute"
 API_WEBSOCKET = "/api/media/ws"
+API_BROWSER_FOLDERS = "/api/browser/folders"
+API_BROWSER_BROWSE = "/api/browser/browse"
+API_BROWSER_PLAY = "/api/browser/play"
 
 # Service names
 SERVICE_EXECUTE_SCRIPT = "execute_script"
+SERVICE_PLAY_MEDIA_FILE = "play_media_file"
 
 # Service attributes
 ATTR_SCRIPT_NAME = "script_name"
 ATTR_SCRIPT_ARGS = "args"
+ATTR_FILE_PATH = "file_path"