What version of Safari are you using? You posted System Preferences is set to allow cookies. Is Safari/Preferences/Privacy set to allow cookies and have you tried unchecking Prevent cross-site tracking?
Is this happening on all web sites or only some web sites? If you are using Safari version 13.0.4, others are seeing the same thing. It seems to be a bug in the newest Safari 13 version.
Block cookies is off but being limited by… - Apple Community
Try another browser until the problem is fixed.
Firefox 10.9 or higher
Opera Browser 10.9 or higher
SeaMonkey 10.9 or higher8
Waterfox 10.8 or higher
You can also try Safari Technology Preview. Go to Safari/Preferences/Advanced and check Show Develop menu in menu bar. Go to the Develop menu and select Get Safari Technology Preview. Open from the Applications folder.