We have been using the CMS for years. Overnight, the CMS list started showing the staging domain, and when we try to edit any page, the Publish option is disabled.
Thanks, @Gaurav_Aggarwal, but those settings had been working correctly for years. I'm the only person maintaining this website, and nothing was changed.
I've contacted support and passed to another level. It was corrected after a while.
I don't know what caused it. It was "fixed" (as in returned to the previous state, all pages pointing to the correct domain) within an hour of creating the ticket through online chat.