I can't log into my iCloud because it is sending an authentication to my phone that is broken
I can log into my iCloud because it is sending an authentication to my phone that is broken and my only device
[Re-Titled by Moderator]
See if anything here helps. If necessary, you can use account recovery as explained in the link at bottom of the article.
Verification code - how to get one and sign in with two-factor authentication.