That’s a SEM which is significantly lower resolution, but lets you zoom in and out across a huge range.

STM on the other hand is for looking at individual atoms so coating a surface is just going to show that coating. https://en.wikipedia.org/wiki/Scanning_tunneling_microscope

That's for SEM. I've never heard of sputter coating used for STM.

You are right, I got those two methods mixed up. It looks like gold sputter coating would be a good solution for the home made tungsten STM tips mentioned in the link.