I put the rel = icon link in the HTML with an icon size of 48 px, I tried with .ico and .png but the custom main site icon does not appear in the Google search result (mobile). I requested to reindex in Search Console, but I had no luck. I know I asked to reindex so many times every time I tried to change the link alternatives. By the way, I can see very well the icon in the browser tab and the Google mobile shortcut thumbnail.
Meanwhile, I installed WordPress in the domain subfolder and set the icon, for only a couple of days the icons appeared. So I copied the rel = icon link from WP to my personalized main site, but I had no luck. It still shows the default world icon.