Please notify your email provider. Your message references the MX record and that is a setting on the providers email server, nothing that Thunderbird touches.

David, I understand that. But I have no control over what my email provider (siteground) does. Can I somehow "fix" that in Thunderbird? For example deleting the existing email accounts and then creating them again.

Ok, please post screenshot of your SMTP server settings pane and that may generate ideas. There is still the possibility that Siteground has an error in your account, but we can try other approaches first. It does appear that something has changed. That screenshot may help. Thank you

I deleted and then added back [email protected]. It worked fine, and now I can send from and receive to that address in Thunderbird. I tried the same thing for [email protected] but got this error message after "checking password...": Unable to log in at server. Probably wrong configuration, username or password.

I went into my email provider (siteground) and changed the password for [email protected]. Then again added [email protected] into Thunderbird and it worked! I had mis-remembered the password for [email protected].