I believe stone could be one of the oldest sustainable material as the mechanism of earth building is a continuous process of rock formation, consumption and sustainable regeneration.
In my opinion, stone / marble is a sustainable material only if it is left where it is, in stone / marble quarries. Marble extraction, exploitation, cutting, polishing, transportation are very much energy-consuming and unsustainable operations, therefore the end-product becomes expensive and unsustainable, even if we speak about marble waste for handicraft products.
Shortly, using marble waste is sustainable. In 1994, the International Council for Research and Innovation in Building and Construction proposed a three-dimensional sustainable development framework: Materials, Resources, and phases. Regrading to materials, one sustainable strategy is waste reduction, thus using marble waste is for sure a sustainable technique.
By it self marble waste is sustainable. But not necessarily zero-waste. The processes and other materials (how you make the waste into a solid) needed to make it into a table require more thought.
In addition to the usual design requirements for a table it must remain safe for eating and the necessary repeated cleaning.
Both you and your clients are isolating a single material. In my opinion, missing what a restaurant table needs to do. Start there, agree on needs, then see how marble waste fits into zero-waste and “sustainable enough” in a restaurant environment.