Favicon is not working outside of the Community
For the Favicon to work, I had to upload my image to the orgs assets library: Under Branding>"Select an image to generate a palette" :
Only then was I able to reference my icon, which I had to upload as a 16x16 png image.
Finally, I was able to reference it using the file-asset's relative path as follows:
Notice that the icon name when I reference it has a versioning appended to it,
<link rel="icon" href="/file-asset/coveofavicon?v=1" type="image/png" />
You can use your browsers dev tools to identify the relative path for your community assets, for reference purposes, here is another link provided that helped resolve this:
<link rel="icon" href="/sfsites/c/file-asset/Favicon_FileName?v=1" type="image/png" />
I did not find this documented anywhere =(, hope this helps other people.
This will change some of your community stylings, since it will detect the colors your image/favicon uses, however, this is easily reversible by re-selecting the original colors you had under the branding option.
For the Favicon I would recommend to use some public service which can host the image and provide https url of the image rather than using images from static resource and using different set of urls
<link rel="shortcut icon" href="https://static.url" id="favicon-ico">
I think the issue might be the url is wrong in your case .You might want to open browser console and check the error
Try using a relative url like below
<link rel="shortcut icon" href="/resource/Comm_resources/images/headFavicon.ico" />