Thank you so much @fronzbot for the update to handle the changes to authorisation! I updated Home Assistant, clicked accept in the email Blink sent me and everything just works again 
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In regards to my doorbell script, I was able to exec into my Home Assistant docker container to run the script manually, I clicked accept in the email, skipped the code prompt in the console and the script completed ok. As expected, if I run it again it no longer prompts for a code (as it’s been authorised previously).
I’m not sure what identifier has been authorized here and there’s the possibility that whatever it is might change. So I’m thinking I should call the Blink class with no_prompt=True. Then, my presumption is that, if the identifier does change I’ll just get another email, the script will fail that run but will be ok on the next run. Does this logic sound correct to you?