Introduced with 7f3aa617ce
The `PaintMode` is needed when activating the default tool. There were
two things that caused this field on the `PaintRuntime` to be in an
invalid state on duplication:
* The original values for `PaintRuntime` were not copied to the new
instance.
* When copying `ToolSettings`, the incorrect old value of `Paint` was
passed to `BKE_paint_copy`, leading to the inability to copy the right
data.
Pull Request: https://projects.blender.org/blender/blender/pulls/146199