I've recently migrated a website of mine to https and now the favicon in Google's search results shows the general globe instead of the site's favicon.
This is how the favicon is defined:
<link rel="shortcut icon" href="/wp-content/uploads/fbrfg/favicon.ico">
The favicon is actually defined the same way as the http version of my site, I've made sure that it is accessible and the favicon is shown correctly on Chrome tabs.
I've also made sure that the main page of the website is indexed in Google Search Console.
Pages that still show up in the search results with their http version (yet to be crawled), have the correct favicon.