Welcome to Stackoverflow! You're in the right place. The $brand-color
sass variable is used for the body background.
A local test showed the background color change
Simply changing the color value worked for me with no issue.
Here's what I did:
Cloned the project
Changed the color value from $brand-color: #fede00;
to $brand-color: #6e6e6c;
in the _sass_variables.scss file
Stopped and restarted the Jekyll server

A test using GitHub pages
After cloning your project, I had some issues building it locally. I removed the gemspec file and fixed your Gemfile. I saw the same color, which was working fine locally.
The fix: Change the URL and baseurl parameters
Finding the reason for the non-changing color on GitHub pages took some time. Finally, I found out that the URL for the CSS in the index.html file was the page from the original page author :
<link rel="stylesheet" href="https://patdryburgh.github.io/assets/css/main.css?1672179035996506134">
The reason was that the CSS URL in the default layout uses an absolute URL (see here).
I could fix the absolute URL issue by changing the baseurl and URL keys in the _config.yml file:
baseurl: "0xtetus.GitHub.io"
url: "https://cadamini.github.io"
In your case, reconfigure the _config.yml file as follows:
baseurl: ""
url: "https://0xtetus.github.io"