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/api_client.py

@@ -27,6 +27,9 @@ from .const import (
     API_TOGGLE,
     API_SCRIPTS_LIST,
     API_SCRIPTS_EXECUTE,
+    API_BROWSER_FOLDERS,
+    API_BROWSER_BROWSE,
+    API_BROWSER_PLAY,
 )
 
 _LOGGER = logging.getLogger(__name__)
@@ -296,6 +299,49 @@ class MediaServerClient:
         json_data = {"args": args or []}
         return await self._request("POST", endpoint, json_data)
 
+    async def get_media_folders(self) -> dict[str, dict[str, Any]]:
+        """Get configured media folders.
+
+        Returns:
+            Dictionary of folders with folder_id as key and folder config as value
+        """
+        return await self._request("GET", API_BROWSER_FOLDERS)
+
+    async def browse_folder(
+        self, folder_id: str, path: str = "", offset: int = 0, limit: int = 100
+    ) -> dict[str, Any]:
+        """Browse a media folder.
+
+        Args:
+            folder_id: ID of the folder to browse
+            path: Path within the folder (empty for root)
+            offset: Pagination offset
+            limit: Number of items to return
+
+        Returns:
+            Dictionary with current_path, parent_path, items, total, offset, limit
+        """
+        params = {
+            "folder_id": folder_id,
+            "path": path,
+            "offset": offset,
+            "limit": limit,
+        }
+        query_string = "&".join(f"{k}={v}" for k, v in params.items())
+        endpoint = f"{API_BROWSER_BROWSE}?{query_string}"
+        return await self._request("GET", endpoint)
+
+    async def play_media_file(self, file_path: str) -> dict[str, Any]:
+        """Play a media file by absolute path.
+
+        Args:
+            file_path: Absolute path to the media file
+
+        Returns:
+            Response data with success status
+        """
+        return await self._request("POST", API_BROWSER_PLAY, {"path": file_path})
+
 
 class MediaServerWebSocket:
     """WebSocket client for real-time media status updates."""