I am having the same issue since about a week ago. If ADP is enabled, I cannot load encrypted iCloud.com apps like Photos or Notes. Doesn't work on Chrome or Edge on my Windows PC nor Chrome or Safari on my Macbook Pro (which rules out a Chrome or Windows update breaking something). All my devices are updated to the latest versions of the OS and apps.
So it seems like a backend problem since everything was working fine and then suddenly stopped working on both my Mac and my Windows PC. Strangely, you're the only other person I can find with the same issue -- doesn't even seem like there are any posts about it on Reddit.
Sometimes when trying to access Photos or Notes it does give me an access code prompt on my iPhone, and I approve it, then iCloud.com on my PC or Mac kicks me immediately back to the iCloud.com login screen (not the dashboard).
Other times, I get the "Sending access request..." and then immediately "There was no response to the request sent to your devices." and nothing pops up on my iPhone, iPad, or Mac.
I was on the phone with Apple for an hour today, they are gathering some data and sending it up the chain to engineering. No fix yet. I have a followup call with them on Friday morning. I'll post if they provide a solution, but I'm guessing the problem is 100% on the backend of iCloud.com