I have never tried this for such a huge amount of rasters; hope this works:
GDALTileIndex (Raster > Miscellaneous > Tile Index) on your raster
Centroids (Vector > Geometry Tools > Centroids) on the tile polygons (from Step 1)
Add Geometry Attributes (Processing Toolbox > Vector geometry) on the centroids (from Step 2)
Numbers that big are going to be small units like metres or feet.
The earth circumference is about 40,000,000 m, so your numbers might be about 15,000,000m east and 4,500,000m south of some origin point.
The most common coordinate reference used these days is Google's Web Mercator system. I can use R to see where your point is in latitude-longitude:
Tile services typically (not always, but almost always) use the Web Mercator projection (3857), because it has nice properties for tiling. It's a safe assumption.
In this case, you don't need to assume, since it's in the metadata for the service: https://services.arcgisonline.com/ArcGIS/rest/services/World_Topo_Map/MapServer/
This tile pattern (z/x/y) is ...
Found out the solution. The shapefile was read only, I couldn't figure out how to edit the attribute table or create new features. In order to remedy this you have to exit ArcMap. Open the file explorer (or ArcCatalog) go to folder containing shapefile > properties > uncheck read only. Once the shapefile was editable a tool called "Add XY coordinates" was ...