The email never arrived, I checked the spam folder and all that. After a while I clicked "Send a new code" and got the error "Select a valid choice. 0 is not one of the available choices." Oooooookay. I cleared cookies etc and tried again, and it continues to demand, while failing to send, a confirmation code. But this second login attempt did cause them to send me an automated "New login to Instagram" email.
Lastly, I clicked the Get Support link, and it just pops a dialog that says "If you’re unable to get the security code, you need to use the Instagram app to secure your account." I do not have the Instagram app, and newly installing it while my account is locked would be pointless.
So, I guess that account is unrecoverable now. Great work, Meta.