Is there nothing to say about nothing
Thank you for your detailed account of how numbers can be derived from empty sets and I don't doubt that modern mathematicians consider it fundamental to mathematics, and even most physicists too.
However in terms of the philosophy of mathematics, does it actually achieve anything?.. well that depends upon what you are trying to achieve.
It would seem that they are trying to ling mathematical 'objects' to real objects in a logically rigorous way. But I don't believe that that is the best way to go.
First off why should a set of nothing be any more fundamental than zero or even 1.
Second it creates a mountain out of a molehill.
Mathematics existed and was eminently useful long before anyone invented the concept of 'sets'
what is meant by an 'object' anyway? It is just a label or category if you like for those things that are considered to have objectivity.