Just noticed the ambiguity in my question re: message types. When I talk about message types, I was referring to different types of application messages, not ordinary message types such as "binary" or "text." So I marked @PavelBucek's answer as accepted.
However, I tried an experiment with Glassfish and had two endpoints. My suspicions were correct and that a TCP connection was established on each connected endpoint. This will result in more server load if more than one websocket endpoint is used on the same page.
Thus, I came to the conclusion that there should only be one endpoint for processing application messages, provided that everything is the only native type.
This would mean that the application must dispatch and not rely on some higher level API to do this for us.
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