To a server, your character is just a few lines of information. the less information you need to send and receive, the lower the latency and the more you can fit on it. It only takes fractions of a second to send this amount of information.
Things like the UI and graphics are all processed at the client side meaning the game only has to deal with a string of information that is moving along a 2d or 3d grid and interacting with other lines of information. Something even a desktop PC can do many, many times per second without issue.
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