Does Lightroom CC (not classic) have HDR processing? I cannot find it anywhere, and there is almost no information out there about it.
You can't find it because it isn't there. You need Lightroom Classic CC to have HDR.
If you have installed Ps you can export from CC and use the HDR feature there. The edited HDR image will be stacked with your original. While it's not accessible on a smart device it will work quite well on your desktop version of Lr Cloud.