In the following example you can see how to change site logo image URL only on home page of your website, Other pages will get logo from theme options.

In filter name you can change xtra/option/logo to modify another option, for example for modifying layout value, try xtra/option/layout and return your value.

Best solution is to add custom actions and filters in Child Theme functions.php file. But also you can create your own plugin and use this codes in your plugin.

In the below screenshot, you can see how to find site width option key. First open your customizer page then find your option and then open your browser inspect element feature to find the input name or data-depent-id attribute. Exactly like below shot you can find key. For site width key is site_width