Multiple buffer ring area analysis using ArcGIS Pro

I have some sites what I’ve created multi ring buffers for in one shape file, each ring is 50m from the center up to 1000m. The file is one shapefile with many polygons and each ring is the full size (no dissolve).

I have three different polygon shapefiles that I want to overlay and find the area of each circle they take.

So for example I want to know the area of canopy cover(green layer) over the 500m circle for site 1. but for every circle

I tried doing an intersect of the two layers but it comes back with a lock error and an empty attribute table.