I have had only limited contact with kahr support, but that experience was much better than you describe. Not doubting you....just adding a data point. Would it be possible for you to post a picture of the broken part and perhaps the parts they sent? That might help sort things out here.

I am at a loss to figure out how tapping or pushing on the slide stop to remove it could cause it to snap, unless it was simply a defective part. Even then, if it snapped apart like a caarrot that would suggest some sort of lateral pressure, whcih should not be part of removal or reinstallation. I also cannot understand why Kahr could not figure out the part you need. I wonder if perhaps there is a communication error here? I assume by slide stop pin you mean the slide stop itself, right? Or were you removing something else like the retaining pin for the slide stop spring?

Worst case, you might need to send the gun back to kahr and they will fix it, but I am hoping people here can help you get this sorted.