Hi,
The 2 sites don’t use the same version for the menu-icons plugin (font awesome). The live site uses 5.5.3 while the staging site uses 5.6.
Plus the live sites adds this in while the staging site doesn’t: <link rel="stylesheet" id="font-awesome-shims-css" href="https://use.fontawesome.com/releases/v5.15.2/css/v4-shims.css?wpfas=true" type="text/css" media="all">
We’re not exactly sure why and this isn’t something the theme controls. It’s best to ask the plugin developer for this particular issue.