How do I do polygon ownership shading?

There are a number of issues with your request.

1. In general, OSM is not interested in ownership or parcel data, especially when this information is not visible on the ground. (If there's a fence with a sign "XYZ property" then that's a different matter.) OSM might, however, be interested in areas that have a certain protection status or other characteristics that we do record.
2. If such data is retrieved from a third-party source, the license situation must be checked. Probably not an issue in the US but best be safe, ensure that the source doesn't claim a copyright on the data.
3. Simply uploading polygons leads to low-quality data, where the boundaries of neighboring areas (say, a state park and an Indian Reservation) overlap or leave little gaps when in reality one starts exactly where the other ends. Or, a state park ends exactly at the river, but because the river was traced from imagery and the state park imported, they don't line up or overlap in OSM. In the worst case, you'd be uploading an object that already exists in some form and you'd duplicate that. You would be expected to fix all these issues before uploading.
4. Even if the data were in OSM, you wouldn't get to color-code it in OSM; you'd have to run your own renderer to define which kinds of areas to use which color for. And if you do (run your own renderer) then you might not have to get the data into OSM in the first place, you could just configure your renderer to read it from a shape file on disk. (Another option of drawing stuff on top of OSM, including ready-made third-party GeoJSON files, is the "umap" service on umap.openstreetmap.fr.)

See https://wiki.openstreetmap.org/wiki/Import/Guidelines for more on importing third-party data to OSM.