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> no one would seriously think today that our math is deeply inscribed in the essence of reality

This is straight up wrong; most physicists I know, regardless of subdiscipline, basically agree on some variation of the idea that reality is somehow underpinned by algebraic structures.

Reality is just a convenient tool with which we can discern mathematics.

> the paper shows a very weak statistical significance

How so? The p values are quite low.

They're not low enough to account for the look elsewhere effect[1] (known by a different name in this field, but the idea is the same). In this case they look at 500,000 measurements so finding p-values of 10⁻⁵/10⁻⁶ is expected.

[1] https://en.wikipedia.org/wiki/Look-elsewhere_effect