I don't think that's accurate. We can pretty carefully calculate the forces involved and answer the question as posed. Related: We can calculate how strong a magnet has to be to hold your artwork on the fridge in opposition to the force of Earth's gravity.

The GR vs Standard Model breakdown occurs at the extreme limits of GR, for example Planck scale regions of space and black hole singularities. A heavy nucleus is way too big to probe these limits and is well within the domain of physics where we don't see a conflict between the two theories.

> string theory has currently failed to combine them in a testable way

String theory may well be wrong/currently untestable, however failure to invalidate the null hypothesis is not proof that somehow we don't have a meaningful understanding of other, proven theories/laws.

Put a different way, if an apple falls from a tree on earth, I don't panic because I don't understand quarks or electron orbitals. I calculate the point/speed/force of impact to acceptable margins of error.

I think the point is that string theory is a huge model with so many parameters that it can fit everything. This is overfitting. Because of that it does not have predicting power.