How can I add a section with a different background color?

If you’re using gutenberg choose a “group” block. You’ll be able to set the background to any color you would like. If you want the group to span the width of the page you’ll need to set the alignment to “full-width”. When you hover over the block itself you’ll get a toolbar pop up. Make sure you’re on the “group” block! Then look for the alignment icon and choose full width.

If you’re looking to put content into the group and want it contained, add whichever block you need into the Group.