Thanks for the detailed reply.
First the good news: I clicked on [constrain] and messages were listed.
Now some additional details which may help anyone looking into this.
Throughout all my various attempts at using different links, URLs and logging in and out (detailed in the OP), I made no changes whatsoever to anything in "Message Settings" or "Message Inbox".
In "Message Settings", I have "/msg me when there's a reply to one of my posts" checked and three folders (Deleted, Inbox and Archive — listed in that order); everything else in either unchecked or blank.
In "Message Inbox", I have "To kcott" and "Inbox (n)" checked; everything else in either unchecked or blank.
Prior to clicking [constrain], I had messages in all three folders: Inbox (2); Archive (119); Deleted (3). [Guess: the code behind this part of the site either "saw" all of those as unchecked or "saw" some other combination which generated an empty list (e.g. I just tried "From kcott" and "Deleted", which listed nothing).]
Any changes I may have made to "Message Settings" would have been years ago; certainly nothing recently.
I only rarely change the "Message Inbox" settings. I don't recall listing deleted or archived messages recently but may have done.
I nearly always access "Message Inbox" via the CB link (with srch_folder=0): your comment about this resetting the options sounds about right (but I'm guessing a bit there).
I use "Message Inbox" frequently (often several times a day) and haven't seen this behaviour previously. I'd consider myself reasonably proficient in its use.
That's all I can think of that might be helpful: happy to provide more on request.