Take a look at this test server (it is for a C library, but it doesn't matter for the moment).
If you enable the Developer Tools (F12) in your browser, you are able also to track the timing of websocket data packets
For example this is a test with my browser and my actual connection (with a ping to DNS of 10ms).
The libwebsockets server is located in France while I'm in Italy: the measured time is for a request starting from my browser -> to server -> back to my browser
I don't know if with ESP32 you can achieve similar perfromance, but for sure WebSocket is one of the best options you have with your needs.