Why is the first line, that has the query executed, saying that the command tag is "idle", shouldn't it say "SELECT"?
"Command tag: type of session's current command" - given your example I suppose this means "initial state of the session" as opposed to being a category tag of what the current line is doing. What you are seeing is "start at idle and parse" the incoming statement text. That is one action - parse. The subsequent action is "execute" the contents of the SELECT that is now in the active state of the session.
If the above is correct the docs could be more clear since I'd agree that your interpretation of the field seems more logical - though knowing initial state is quite useful in its own right.