Common problems I see in the Webflow forums;
Assuming you've uploaded your favicons in your General site config, and published your site, you should be fine.
If you're still not seeing it, clear your browser cache.
In 99% of the situations I've seen, most likely, you have a 16x16 icon specified in your favicons. Google doesn't like this, and ends up not showing any favicon at all.
Google looks for and updates your favicon whenever it crawls your home page. If you make changes to your favicon and want to inform Google about the changes, you can request indexing of your site's homepage. Updates can take a few days or longer to appear in search results.
SOLUTION: Most likely, you can define your favicon directly in the HEAD of your login page. [ untested ]
https://discourse.webflow.com/t/make-title-favicon-and-share-image-of-a-password-protected-page-visible-when-sharing-the-link/176185
https://discourse.webflow.com/t/my-password-protect-sites-favicon-image-not-showing-when-link-is-shared-through-messages/158341