Your logic is flawed.
First, you are wrong that Sagan's dragon analogy only applies to claims about hidden physical objects. This is a strawman. What the analogy is actually arguing is that if a claim is constructed so that no conceivable evidence could count against it, then belief is unjustified. By restricting the analogy to the physical only, you are narrowing its scope unjustifiably and avoiding the real epistemic challenge.
Second, your argument assumes either a claim is empirical or it is purely metaphysical and therefore immune to evidential critique, but many metaphysical claims have empirical implications and interact with empirical facts (e.g., causation, contingency, cosmology, consciousness) If God is claimed to be the cause of the universe, the ground of all existence, and active in reality, then the claim is not sealed off from evidential scrutiny, even if it is not directly observable.
You say that “Demanding physical tests is a category mistake.”, but I'm not asking for physical tests, I'm asking for evidence and this can be logical, explanatory, predictive and comparative (vs rival metaphysical explanations).
Finally, you are begging the question by creating a premise that already assumes the truth of the conclusion, creating a circular argument that offers no real proof. You assume that every contingent chain requires a necessary being, the necessary being must be personal or God-like, and the necessary being is a coherent metaphysical category, but none of these have been established. So “Therefore a necessary, non-contingent being must exist.” only follows if one already accepts that everything that exists or happens must have a sufficient explanation or reason why it is so, that facts must have an underlying reason, and cannot be just facts, and that the explanation must terminate in an entity rather than a fact or law.
By declaring “You can’t refute a metaphysical argument with empirical analogies”, the argument effectively removes itself from any external critique except from within its own framework, which is the exact problem that Sagan highlights, claims structured so they cannot be tested, challenged, or falsified are indistinguishable from false ones.