Not sure I can come up with anything that has not already been suggested and tried, but here goes:
Are you absolutely certain that eBay is sending the code to the correct email address?
If so, check to make sure your email provider is not blocking the emails or sending them to a spam folder. If you have an option to view all mail messages, check that to see if the eBay emails can be found that way.
Is it possible you already had more than one account, and you have changed the password of another account? Have you tried signing in with your original password? Try another browser or another sign-in link to rule out browser issues or a bad sign-in link. If you have the eBay app on your phone, check to see if you are still signed in.
If you have Google, Apple or Facebook accounts linked to your original eBay account, try signing in using that method. Note that if the accounts are not already linked, you may inadvertently create another account by signing in that way for the first time, so only try that if you have previously used that method to sign in to your account, and make sure you are using the correct Google, Apple or Facebook account when signing in.
Is it possible your account was hijacked? If your email address was changed by someone else, then that would explain why you are not getting any codes.
If you have been on the phone with eBay for multiple hours, I would think that most of these options would already have been covered, but there is always a chance that one option was overlooked.
There are text-to-landline services available from many phone providers; if you have such a service and someone sends a text to your landline number, you can receive a voicemail message of the message text. Check with your provider to see if that option is available for you. If so, you may be able to bypass the problematic email and send the text to your phone.
