Google can show your favicon in the search results next to your search result snippet. Google’s John Mueller said Google finds your favicon based on the favicon presented on your home page only.
John wrote on Twitter “Last I checked, I think we only picked up the homepage favicon.”
So I guess if you use different favicons on different pages of your website, then Google will ignore the other pages and just use the home page’s favicon for the favicon it displays in the search results. Although, I am not sure if I have ever seen a site use different favicons on a page-by-page basis – have you?
Here are those tweets:
Last I checked, I think we only picked up the homepage favicon.
— ?〈link href=//johnmu.com rel=canonical 〉? (@JohnMu) September 14, 2022
Forum discussion at Twitter.