Joystick Controller - Web Server - Unity Game

I suggest old fashioned debugging using serial monitor and Serial.print.
In the device sending data, print when it is ready to send, if it has to wait for the channel to be free etc.
In the receiving device do the corresponding thing, print when the loop asks for data....
If You include the value of millis() in the printout maybe You can see something. Is it the sending side or the receiving side?
Could using a hard wired digital test line between the sender and receiver add debugging? Like the sender sets the test signal active when a message is sent and the receiver somehow reads this and starts an internal timer.... That would tell how slow/fast the cloud/server is.