#'arg is a syntax object, therefore (number? #'arg) or (string? #'arg) will always be false. If you are trying to dispatch based on literals, you could use e.g. (number? (syntax-e #'arg)) to identify a numeric literal. But it is not very common that a macro handles a numeric literal differently than an identifier that is bound to a numeric value at runtime. I'm guessing you can use a regular procedure and cond for most of this.
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