You cannot respond by email to a ticket from a different email address. This would be why you are not seeing updates on your existing tickets. We strongly recommend against running the email server for the address associated with your account on a droplet on that account as it can cause this situation. Recovering an account if you do not have access to the account email address is a manual process. You can start this by sending a new email to contact@digitalocean.com from another email account.

A much quicker option to recover access is to:

1.) Sign up with a free domain email host like Zoho
2.) Point your domain’s MX records to the new service
3.) Re-create the currently inaccessible email address on the new service

This will allow you to receive the needed code without having to verify ownership of your account manually. Once you have the code and can log in you can get your email server back up and switch back your MX records if you want.