If you have set a Favicon using ShortPoint Theme Builder, but still see the standard SharePoint icon in Microsoft Edge, this article should be helpful for you.
This known issue of Microsoft Edge reproduces in SharePoint Online (Office 365), SharePoint 2013, SharePoint 2016 and SharePoint 2019 environments.
You can see the correct Favicon in other browsers, for example:
There are particular issues with Favicons in the Edge browser outside of our control. Using the workaround described below will help you to resolve the issue.
To fix this issue you will need to have an image URL from the external hosting web site. Please, follow the steps below.
Step 1. Prepare the image URL
Please upload the image you would like to use as a Favicon to reliable external hosting and copy the image URL. You might want to check this article for a more detailed instruction.
You need to set the public permission, so that this image will be accessible (everyone can view it and/or find on the Internet).
Note: We won't recommend any specific software here. Please use the one you find good for you. However, we suggest you to host the image at a reliable hosting so that you can control it (e. g., nobody can delete it).
For example, the image URL we would like to use as our Favicon is:
Step 2. Paste the image URL to Theme Builder
Open Theme Builder.
In Office 365 and SharePoint 2019, go to Site contents > ShortPoint Dashboard > Theme Builder and click Customize my site:
In SharePoint 2013 and SharePoint 2016, go to Site settings > ShortPoint Dashboard > Theme Builder and click Customize my site:
Go to Header > Logo. Paste your image URL to the Favicon field and click Publish:
That's it. Now your Favicon is displayed in Microsoft Edge: