Google has updated its favicon search developer documentation to now say that you don't need to host the favicon in the same domain in order to be eligible for a favicon in Google Search results. Google removed the line, "the URL must be in the same domain as the home page."
Here is a screenshot of what changed in the old documentation:
Google posted "February 23: Removed the hosting location requirement from the favicon documentation; you don't need to host the favicon in the same domain in order to be eligible for a favicon in Google Search results."
So you no longer need to ensure the favicon is on the same domain as the site to be eligible to show a favicon in Google Search.
This is really cool & @okaylizzi is awesome for looking into this. It could save people a lot of wasted time. I noticed favicons *were* showing up when NOT hosted on the same domain as the homepage. Ends up you can host them anywhere. So that's one less thing to worry about. :) pic.twitter.com/Afa1JsK9jg
— Glenn Gabe (@glenngabe) February 23, 2023
Forum discussion at Twitter.