Does the Peano axiom of reflexivity ∀x(x=x), in that the statement 'x=x'is a tautology and contains no information, imply that mathematics lacks ontological reality? By this I mean that if the 'building blocks' of mathematics are empty of information from their own frames of reference, does mathematics then provide truth only within an ontologically relational framework?
The axiom of reflexivity, specifying that equality is reflexive, simply helps define one aspect of the '=' symbol. This helps make a connection between well-formed formal strings that use that symbol and our personal conception of what equality should act like. It only seems boring and tautological because the concept is obvious, but the axiom is needed to operate on the symbols usefully. The axiom contains quite a bit of information ('usefulness' might be more appropriate) because without it, all sorts of theorems about natural numbers could not be proved.
I don't know what you could mean by 'empty of information in their own frame of reference'. You're using words that don't have any technical relevance to axioms and proof theory. If you're using them non-technically, you'd really have to explain what you mean by 'information' and 'frame of reference' as they refer to the mathematical system.
But does 'mathematics then provide truth only within an ontologically relational framework'? Whatever you think about those words together, a yes or no answer to it will only justify some hidden personal definitions to make the answer right.
But to jump from the axiom that equality is reflexive and that it feels tautological all the way to a statement about all of mathematics and reality (and ontology) is just perverse. The axiom is included to make proofs work (if you do some examples you'll see where the axiom comes in useful). If you want to draw the earth-shattering consequence that there is no absolute truth, the seeming tautology of reflexivity in arithmetic is not the place. (on the other hand, truth is undefinable inside arithmetic, but that's not the truth you're thinking of)
To help with this, is there anything special about reflexivity axiom? Aren't symmetricity and transitivity also tautological? What about the other axioms? Axioms are often very boring because they should be intuitively non-questionable (in order to trust that the proof system is proving things that fit with your intuition).