Pixel count for Barren Soil

One way is probably to integrate the threshold directly in the custom script, i.e.:
if (val> threhold) return [1]; else return [0];
If I remember correctly, you can then use bins=4 in FIS and still get only two bins.

The better way would be to make use of Statistical API, where you can define custom bins:

Statistical API

Our powerful Statistical API makes it possible to get various statistics for satellite imagery without having to download images.

Thanks for your feedback, seems to be working well,
But I find the count result of the FIS bins to be strange.
I set the resolution to be 10m, so the total count from both 0 and 1 should equal to total size of the polygon, but it does not add up.
I would assume of my polygon is .01 sq KM, I would expect to have a total count of 10000. Am I reasonable to assume this calculation?

It should be like this, yes. There might be some discrepancy if your polygon is not aligned with the UTM grid, i.e. the pixels on the border might sometimes fall in and sometimes not.