Most probably after moving to Office 365- your email is now recognized as Azure AD account & you are authorised by AAD in Your organization. To solve issue- firstly admin of old organization should invite You as guest to "old" organization AAD. Please also follow this link:
https://learn.microsoft.com/en-us/azure/devops/organizations/accounts/access-with-azure-ad?view=azure-devops
I hope this will help