Hi Paul,
I'm the author of Eglot, an LSP client for Emacs whose functionality will soon (ish) be in Emacs itself. It explores a subset of the LSP protocol and leverages it in terms of Emacs functions. You can use Eglot it to gauge how developed a server is. You can -- and emacs-devel is the place to do that -- extend Eglot to explore more of the LSP protocol, provided that the LSP server you're using works in those regions unexplored by Eglot. Not sure if this is what you're looking for.
If you're strictly looking for a list of capabilities offered by the LSP server in question, there is a section in the protocol specification devoted to describing a protocol message with that information. That protocol message is sent early on in the handshake, and you can easily inspect it with the Eglot client (or other clients). Using Emacs or other clients for this specific purpose would be mostly "indifferent" in your categorization.
João