After a day of experimentation, the closest I can get is by doing the following:
- Create a style rule called Tips Heading based on Normal, then set it to be Bold with a blue background.
- Create another style rule called Tips List based on List Paragraph, and set it to have a blue background.
Unfortunately the List cannot be indented because the background colour also indents. The border is also affected in this manner, so I ignored the border and indentation. It works really well and is semantically well structured.