iPhone SE (first generation), iOS 14.4.2 (18D70), iOS Safari
I have regularly used this phone to browse the SE sites in which I'm interested: Travel, Expatriates, Mechanics, Home Improvement, and Ask Different. The phone's now running 14.4.2; over the past months I've updated it promptly as new versions are offered. Keychain takes care of my passwords, and all seemed good.
Today, however, when I navigate to any of these SE sites, I'm confronted with this:
Nothing has changed in the phone's settings, cookies are not blocked. Under the dialog, I am already logged in. Even odder, when I click on "Customize settings" there's a brief rotating wheel symbol, followed by...nothing: the dialog remains in place, blocking the page. I can only get rid of the dialog by clicking "Accept all cookies." The same thing happens on all five SE sites. It isn't happening on my desktop machine.
Restarting (both regular and forced) has no effect, the dialog keeps appearing. And the dialog is persistent — it appears every time the phone loads an SE site.
What's going on here?