I can't access the web icloud drive

I have enabled additional security and want to gain access (with confirmation from the device) to iCloud Drive Web.

I go to icloud.com, select icloud drive, the site says “Gaining access” and on my Macbook in the upper right corner I receive a notification “Temporary provision of access...”. I click on this notification and it happily disappears. “Granting access” hangs on the site for a long time, and then a message appears something like “Access cannot be obtained because the trusted device has not confirmed it.”

I tried restarting the Mac and different browsers, including Safari.

What can be wrong?