I would like to address the matter of setting the icon in the location indicated in the provided screenshot. Specifically, when using a browser window, the default behavior is to display the favicon of the corresponding website.
To customize the favicon of your website, you can access the WordPress settings within the customizer. Check this article for further details: https://www.wpbeginner.com/wp-tutorials/how-to-add-a-favicon-to-your-wordpress-blog/
Furthermore, in relation to the sharing icon for your website, it is managed and handled by SEO plugins such as YOAST or RANK MATH SEO. Within the settings of these SEO plugins, you have the ability to set the sharing icon according to your specific requirements: https://simplesocialimages.com/social-sharing-images/
Should you require any further assistance or clarification regarding these settings, please do not hesitate to reach out.