refactor: remove Discord RPC file logging

Removes file-based logging from Discord RPC manager in favour of using
the tracing framework exclusively. All Discord RPC logs now appear in
the Debug Console with proper log levels.

Changes:
- Remove log_path field and file logging methods from DiscordRpcManager
- Replace all self.log() calls with tracing macros (debug/info/error)
- Remove log_discord_rpc command and its registration
- Remove set_app_handle() call from main setup

Benefits:
- Reduces disk usage (no unbounded log file growth)
- Eliminates maintenance burden of managing log files
- Better log levels and integration with existing tracing system

Closes: #129

src-tauri/src/commands.rs

@@ -1145,15 +1145,6 @@ pub async fn stop_discord_rpc(
     discord_rpc.stop()
 }
 
-#[tauri::command]
-pub async fn log_discord_rpc(
-    discord_rpc: State<'_, std::sync::Arc<crate::discord_rpc::DiscordRpcManager>>,
-    message: String,
-) -> Result<(), String> {
-    discord_rpc.log(&message);
-    Ok(())
-}
-
 #[tauri::command]
 pub async fn close_application(app_handle: AppHandle) -> Result<(), String> {
     // Get the main window