But, is there anything like a theoretical proof/evidence? What would that be? — BrianW

Both formal and informal logical argumentation are what's at play in theoretical evidence.

We know there's empirical proof/ evidence or empirical ways to arrive at proof/evidence. But, is there anything like a theoretical proof/evidence? What would that be? — BrianW

I think that the best “proof” theory can achieve is verification of its reliability. So if you have a theory and you apply it rigorously and it shows itself to be reliably correct, thats about as firm a proof the theory can get.
I suppose what Im saying is there is no proof without interaction with the physical world, to confirm the theories validity.

It seems like the theoretical isn't definitive enough without empiricism. Don't all theories aim at providing practical value? If so, is that what gives them significance? If not, then what is their significance?

It seems like the theoretical isn't definitive enough without empiricism. — BrianW

If theory depends on metaphor and passion, then it would seem to require a significant world to theorize about. If it intends to be true, then it would seem to need other people in that world. Since theory is part of language, we might look into what we implicitly affirm even as we question --the possibility of a listener for one thing and the strange what-it-is-ness of intelligibility.

Don't all theories aim at providing practical value? — BrianW

While this is plausible, I'm not so sure anymore that things are that simple. What about dark philosophical theories like pessimism? I can't remember his name at the moment, but there was a lesser known pessimist who committed suicide as soon as he published his pessimistic philosophy. Death (and our ability to jump into the grave early or to choose war over safety) complicates practical value.

If not, then what is their significance? — BrianW

That seems like a deep question to me. What is significance? What does it mean for something to mean? I don't know, but I think it's a worthy question that opens life up somehow.

Presumably, whether a required proof is logical/theoretical, as opposed to empirical, will depend upon whether the original question is essentially logical/theoretical in nature, or empirical in nature. It is entirely unnecessary to involve questions of "significance" or "pessimism", which will only confuse the issue.

Empirically, in the first really scientific piece of medical research carried out in modern times, the British Royal Navy discovered in the late 1700's that an infusion of fresh lemon juice into the grog ration of its sailors would prevent the onset of scurvy. The research was entirely empirical, because they knew nothing about vitamins. Their proofs are still considered valid today because they used all the standard modern techniques such as control groups and allowance for placebo effect.

On the other hand, consider the proposition that 1 + 1 = 2. It has no proof (or even relevance) in the empirical world; its validity is entirely logical in nature, and conditional upon your acceptance of the Peano axioms of arithmetic:

1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2

But your question has a very respectable philosophical pedigree. For example, the Ontological Argument attempts to prove an empirical fact (the existence of God) by using purely logical arguments. Most philosophers would now accept that that's impossible. Fermi's Paradox, incidentally, fails for the same reason.