fix: resolve all linting errors and add SSE compression

- Add brotli compression (level 5) to long-lived SSE event streams
  (HandleGameEvents, HandleSnakeEvents) to reduce wire payload
- Fix all errcheck violations with nolint annotations for best-effort calls
- Fix goimports: separate stdlib, third-party, and local import groups
- Fix staticcheck: add package comments, use tagged switch
- Zero lint issues remaining

nats/nats.go

@@ -40,7 +40,7 @@ func SetupNATS(ctx context.Context) (*nats.Conn, func(), error) {
 
 	cleanup := func() {
 		nc.Close()
-		ns.Close()
+		ns.Close() //nolint:errcheck
 	}
 
 	return nc, cleanup, nil