> there's typically a 5-7 day gap between updating the robots.txt file and crawlers processing it
You could try moving your favicon to another dir, or root dir, for the time being, and update your HTML to match. That way it would be allowed according to the version that Google still has cached. Also, I think browsers look for a favicon at /favicon.ico regardless, so it might be worth making a copy there too.
/favicon.ico is the default and it will be loaded if your page does not specify a different path in the metadata but in my experience most clients respect the metadata and won't try to fetch the default path until after the <head> section of the page loads for HTML content.
But non-HTML content has no choice but to use the default so it's generally a good idea to make sure the default path resolves.
I think it is from the Internet Explorer days. .ico is an actual icon file format on Windows and IIRC originally the icons were in that format, with support for GIF coming when Netscape supported the feature.
You could try moving your favicon to another dir, or root dir, for the time being, and update your HTML to match. That way it would be allowed according to the version that Google still has cached. Also, I think browsers look for a favicon at /favicon.ico regardless, so it might be worth making a copy there too.