I deleted all SMTP passwords. After restarting the machine today and being asked for the passwords, the program is delivering emails again. The problem is resolved.

The problem came back. This time, I could not resolve it using my method above. I am suspecting this has something to do with my OS configurations, since I also cannot send mails with Evolution.

You said "any of my accounts" at the top. You've shown us only one mailbox.org account. Are your others with the same provider? Do they each have their own smtp set-up?

It's usual practice now for smtp to require and use authentication, just as yours is configured. When used in this way, each account will or should use its own smtp setting, with its own username, usually the whole or part of the associated email address.