I’ve etched a couple of dozen powder coated stainless steel tumblers recently and found that when it comes to laser power, less is more. I’ve done various brands all with excellent results, mostly quality brands with thicker powder coat; I think I caught a glimpse of ThermoFlask logo in one of your photos, I’ve done 8 or 10 of those very successfully. I’ve not done white though, that could possibly require a few percent more power due to reflectivity. Anyway, back to less is more, I posted my process and settings here. Yeti tumbler etching - #6 by bLouChip
Since that posting, I’ve changed from my second pass from being OffsetFill to using a 90 deg Fill scan, basically I have one layer that does CrossHatch Fill pattern, and I add a sublayer to do a Line outline of the shapes after the crosshatch fill. The crosshatch fill is at fine/sharp focus and interval of 67% of my beam width, so 0.09mm interval (I’ve more accurately measured my beam width at 0.13mm since the ref post also). I have a similar dual diode 15W +/-5 as you do.
Finally, another process change comes to mind since the ref post, Dawn liquid soap and water with an Eraser pad brief scrub is a good clean up process, seems to be as good or better than LA’s Amazing stuff.
Less is more.