We started using Fila -chip a few years ago-the master kit has 19 colors- solids and translucent s. We have been able to do some awesome repairs using this kit. The UV light can only penetrate 1/8" into a repair so if your repairs are deeper than that you would need to fill twice with fila chip or fill partially with a different product and top it off with the fila chip.
What I see on your table -I would cut the surface aggressively(you could cut it dry)-but i see some oxidation which you may want to try and remove first.
You may be able to sand/grind down the edge profile to remove some chips.
The larger or deeper ones you can use any product your comfortable using.
Are you going to hone or polish this table.
I would guess they want it honed.
If that is a large pock by the corner you could fill using polyester mixed with grout. Make a form around the repair and place some small stainless screws. Then mix unsanded snow white grout into the polyester which you can add colors to.
That will have to cure overnight and then following the profile sand it down to match the contour of the table.