Using the Posts widget #
The Posts widget has equal height columns by default. You just need to set the background on Style → Box → Normal → Background Color. You can also set the Box Shadow, Border Color and other properties for the equal height box on this settings section.
Do not set the background under Advanced → Background because this section will change the background for the entire widget (the container of all the boxes).
Using the Loop Grid widget #
The Loop Grid widget doesn’t have the equal height columns active by default, but you can easily enable it on Content → Equal Height.
Once enabled, click on Edit Template and wait a few seconds because the Elementor Editor will “reload” to let you edit the “embed” template. Once is loaded, use the Navigator to select the parent Section (the option to select the parent section is not visible on hover on this case, you will need to use the navigator). To change the background, go to Style → Background. You can also change other properties of the box here, like Box Shadow (under Border), the border, etc. Just be sure to set this for the parent Section.