When you update your website's favicon, you may notice that the changes don't immediately reflect in the Safari browser. This happens because Safari might still be using the previously cached or stored version of your favicon. Favicons, surprisingly, have a long and peculiar history.
To resolve this issue and ensure that the updated favicon appears in Safari, you can follow these steps to clear Safari's cache:
Quit Safari.
In the Finder, select Go > Go To Folder.
Enter ~/Library/Safari/Favicon Cache/ and press Return.
Use Select All (Command-A) to select the database and cached items.
Drag these to the trash or press Command-Delete.
Empty the trash.