Shor’s algorithm’s advantage isn’t proven, but a proof that integer factorization doesn’t admit a classical algorithm faster than O((log N)^3) could be found. The same applies for Google’s artificial problem.
An analogy which is closer to Google's experiment: measuring versus calculating the energy gaps in benzene to an arbitrary accuracy.
It is "verifiably" faster to measure those with state of the art "quantum tools" but that does not improve our understanding of other aromatic molecules.
(we may still get some insights about anthracene however)
The googles' advantage can be satisfactorily summarised as "not having to write the problem (ie off-diagonal terms) in terms of a classical basis" -- there is a severe overhead of having to represent qubits as bits.
Still, I suspect that that 13000x came from not putting in effort to implement the aforementioned "minimal structure" in their classical counterparts. They emphasized "echoes" and "ergodicity" & I think the "quantum" can further be dropped :)
In general, I do believe that whatever "informational advantage" we can get from these experiments should likewise be used to improve classical calculations.
As another eg: In the arxiv paper linked by GP they talk about provably-efficient shallow classical shadows
