Hi Clare,
Thank you for posting in Microsoft Community. It's understandable how frustrating it is to see your Hotmail account disappear from your Mac but still be on your phone.
Your account was either removed or disconnected from the Mail app on your Mac, or a new profile was created. The good thing is that since your account is still active on your phone, your emails are probably safe.
I suggest checking your Mail or Outlook settings on your Mac to see if your original Hotmail account is still listed. If not, try re-adding it using your Microsoft 365 login. This won’t affect the data on your phone.
Let me know how it goes. If this helped, feel free to mark it as helpful it might make it easier for others to find the solution too. Let me know if you need anything else! I’m here to help!
Regards,
Carlo