Although I don’t have experience etching with the surface coating of the mugs you reference, I have etched a dozen or so powder coated mugs of various brands, such as Yeti, RTIC, ThermoFlask, 95% ablating the surface to bare stainless steel, then cleanup polishes to 100%. None have been white either, and that may matter due to higher reflectivity of visible (diode) laser light. My laser (Neje A40640) is likely 50% to 25% less powerful than your XTool D1 20W. Here are the etching specs for my laser and cleanup process to etch to a polished stainless steel finish. Give it a try. I found that less is more when it comes to power in this etching case.
Cheers,
Lou