As @Vince already stated in comments, Web Mercator is not suitable for this.
Reproject your layers (Save as...) to a local metric one. Regarding epsg.io this could be UTM Zone 54N (EPSG:3095) for example.
If that example is using AcrMap, you can use the Select by Lasso tool which would capture the desired points.
You could also select the boundary of interest set up a Definition Query. This will only display the boundary polygon of interest. From there, you can use the Select by Location to grab the points within the buffer.
If there are additional points ...
Yes it is much more straightforward with advanced license using near, erase, points to line etc. tools. Anyway the workflow below will work with basic license and it is a good candidate for model builder. Shouldn't be hard to shuffle through 100 polygons. It honors selection:
# find script to convert all building vertces to points