The reason for a brass pulley is far better durability over the softer aluminium type.
Commercial desktop machines use them to preserve the zero backlash benefit of the GT2 tooth profile that deteriorates with wear.
Combined with the mass of the Nema23 rotor, the slight increase in total rotational inertia is worth the benefits the quality pulley for a machine that is working hard.
Not sure where the 7.8mm bore came from, but they fit the 8mm shaft Nema23 1.3nm motor quite nicely. See attached.
It is best to go to the 8mm shaft motor because plenty have snapped the smaller diameter shafts with load flexing fatigue that can be associated with stronger belts & tension.
Robotdigg also has the matching 18mm wide GT2 belt available on request at a reasonable price.
Ron
Try Stock Drive Products:
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Robotdigg also has the matching 18mm wide GT2 belt available on request at a reasonable price.

For Nema17 motors GT2 any wider than 9mm would be completely unnecessary.
This 9mm setup is what I adopted for my Alu Core-XY Printer design using large Nema17’s. (attached PDF)
Due to the increasing PnP head mass (with migrating all the valves & motor drivers etc) I quickly went to some decent power driving the main axis.
Nema23 - 2nm (dual shaft) on the Y axis and Nema23 1.3nm on the gantry X-axis.
My first mistake was to use T5 10mm belt / pulleys initially due to their strength and power handling. Problem is they introduce some small backlash which is not so small for 0402 parts etc.
To maintain the performance and improve the accuracy, the wider GT2 setup was the answer.
I was able to source the wide pulleys and matching belt from Derek with about a four week lead time. (see attached) The Belt is 18mm and compare it to 9mm readily available.
My only advice is to try and start where you want to end up with your design and then work back to the beginning.
Have fun.
Ron