Would 23mg of zinc cause a copper deficiency long term?

Copper. Why are you taking that a dose of copper? It is way above the tolerable upper limit (per National Institute of Medicine )which is 10 mg . Please see below. follow up with MD

https://www.webmd.com/vitamins/ai/ingredientmono-902/copper

https://www.mayoclinic.org/drugs-supplements/copper-supplement-oral-route-parenteral-route/before-using/drg-20070120.