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Although likely, it has to be proven that $\pi$ is normal. However, if $\pi$ is proven to be normal using some method (call it Method $A$), will Method $A$ necessarily be able to prove or disprove the normality any real number?

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    This is very, very unlikely. In fact, I find it difficult to think of anything nontrivial about decimal expansions that a proof for $\pi$ by some method allows (in a reasonably similar way) a proof for any specified real number. Incidentally, the list of Stack Exchange questions dealing with aspects of normality and/or decimal expansion properties of $\pi$ given in my answer to Normal Numbers as members of a larger set? might be of interest. – Dave L. Renfro May 07 '21 at 05:42
  • $\pi$ has been proven to be transcendental. Does that proof extend to any real number? Of course, there is the trivial answer of no to your question or mine since not all numbers are normal or transcendental. – badjohn May 07 '21 at 06:59

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