For developers: The background colour in a paragraph style is controlled through the Shading object. It manages background and foreground colour and texture. The Word object model is straight-forward, but you need to choose the right texture as well as the background and foreground colours.
For developers: how to set the background colour in a table style using the Microsoft Word object model. There are 7 ways to set shading (ie background or foreground colour) on elements of a table style in Microsoft Word. Most don't work. This article describes what does seem to work, and identifies the bugs and annoyances in setting shading in table styles.