> I wonder, which physics claims that space and time don't exist (how could it, "exists" is a metaphysical concept, physics only cares about mathematically describing the world and making predictions)

I think this is a common misconception. Scientific theories provide predictive power, but they also provide explanatory power. The latter has fallen out of favour due to quantum mechanics, despite plenty of good interpretations of QM that provide good explanations, but it has always featured prominently every other scientific theory.

And given explanatory power is important, every scientific theory also therefore defines an ontology (your metaphysical concepts). This too has always been part of science.