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Plugable, Wireshark-style data dissectors would be the best option.

Is there some common protocol that is used for binary communication, or is it all custom? Something like hexview or xxd would probably help generally.

Usually custom, that needs to be reverse engineered (with some help of usually minified JavaScript)

This is one option: https://developers.google.com/protocol-buffers

Chrome developer tools can view binary data transmitted with this approach.

Yes, this is upcoming next as binary preview is pretty bad without it.