The log-in code that is suppose to arrive by email never arrives.

That isn't a Thunderbird issue. Is this a two-step signin to an email account? More details may help.

The only password that Thunderbird can be set to use for itself is one to protect your Saved Passwords. That's all done completely locally to your computer and no code is ever sent.

Do you really mean changing the password for your email provider's account? That password can only be changed on the providers web site. During that procedure they may send you a code, but if you don't currently have valid credentials, most providers will ask you for an alternate way to receive the code, usually another email address or a text message. If you suspect that a code is being sent to the alternate address but is not being received by Thunderbird, use THAT providers web mail to check. If you don't see it there, the fault lies with the sender.

The log-in code finally arrived, it took two hours, but all is ok now.