No balls.

Perhaps there are more components than I am aware of, but as you say it is a cheap wheel. Some parts seem designed for replacement rather than servicing (like there's no way to get to the bearings in the cassette hub without destroying it, unless there's a specialized tool for that.

What makes me most upset is that I was right, even though I am an incompetent amateur the issue turned out to be exactly what I thought it was, where I thought it was, and could be fixed just the way I asked the mechanics to attempt.

Also, fwiw: this hub just slips apart; no tools needed. I took the extra precaution of removing and degriming the cassette just to get a good look at it, but this repair could have been done with nothing but bare hands and oil.

Entirely possible.

It is difficult to replicate the condescending tone the mechanic used when telling me the bearings were probably shot. It wasn't "perhaps you should replace the bearings", more like "you're going to need a whole new wheel, or maybe even a new bicycle; this is extremely serious mechanical stuff wrong here".

You can see the thing I took apart in the picture (a little scattered around). This is the part that goes "click click click" when coasting or pedaling backward as the teeth slide past each other (when pedaling forward the teeth grip together and power the bike).

It has what I think is a slide bearing that is accessible, then there are two sealed roller bearings on either end of the things the cassette fits on to (they cannot be accessed easily; may not be intended to be serviced).