It’s all down to “Treat as specified in Server Manager,” which seems to be either the default or the way an old preference got interpreted after upgrading. First of all, you get to Server Manager by clicking on the “Manage cookies…” button. I’d been looking for something labeled Server Manager and didn’t find anything. Secondly, it seems to mean “Ignore any cookie for a site that isn’t explicitly listed in Server Manager.”
Once I added my.opera.com to the list, I was able to log in.
I may switch to “Accept all cookies,” though, since I’ve finally figured out another cookie issue.
A nice feature in Firefox lets you choose how long to keep cookies: until they expire (which could be years from now), or until you close the browser. You can set exceptions for sites that you want to remember your settings. So sites that require cookies will work, but you can clear out all the junk just by closing Firefox, and it will keep only the cookies you want.
Opera has a similar feature, “Delete new cookies when exiting Opera.” There’s no way to define an exception, but you can fudge your way around it by unchecking the box, then visiting the site, then checking the box again. (That way it’s not a new cookie at the point the feature is turned on.) It’s kind of roundabout, but it seems to work.
Edit: Still trying to work out the settings for third-party cookies. If www.example.com sets a cookie for example.com, it considers that third-party, so if you block third-party cookies, it ignores that cookie entirely. But setting third-party cookies to “Let me choose each time” just seems to accept it.
Sense, it makes not.