WordPress Membership Plugin
Ah, the add-on update did the trick! Thank you very much.
Follow-up note: I hadn’t deactivated any of the Simple Membership add-ons as part of the incompatibility testing, but just tried disabling the SWMP Full Page Protection add-on. That removed the full-site lockdown. That is the add-on that I had checked the settings of to be sure the URLs I’d set to be locked are still accurate, which they are. With the add-on deactivated I also tested logging in to a SM account, which worked, so other features are likely still functioning.
With this new result, my question may more specifically be: is the SWPM Full-Page Protection add-on not PHP 8.1 compatible?