In this post I answer the question: “I would like to change the background color of my site header”.
I would first check which theme you are using.

My quick way: check the html source (usually right click => view page source). Searching for “wp-content/themes/” would give me an instant clue.
I would also cross check with one of the online Theme checkers online. E.g. reveals is using Elementor.

How to proceed next, depends on the configuration of the website.

My preferred way: “The Theme way”
If the theme builder provides a way to do change the background color of the side header, I would recommend that first.

Other way: “The CSS way”
If they already are using a Child Theme, I would suggest to add the CSS over there. If not if the Theme provides a way to add custom css.

Make a Child Theme using one of the Child Theme plugins and custom the CSS.
Though having child theme purely for styling is not my preferred solution because that way: styling configurations might be too much “all over the place”.