Hello
Good day! Thank you for posting to Microsoft Community. We are happy to assist you.
Based on the information provided, you are having some issue accessing your mailbox via Outlook Web App and got UserHasNoMailboxAndNoLicenseAssignedError.
For this issue, there is some possibility that your account has not been assigned the Exchange Online license, so that you could not access OWA, please contact your tenant admin to confirm whether your account is licensed correctly.
For your reference: Add users and assign licenses in Microsoft 365 - Microsoft 365 admin | Microsoft Learn.
If the account is licensed correctly, please note that the license needs some period to replicate, sometimes it will take up to 72 hours to replicate in the system, so if it's a new created mailbox, would you please wait for some period and try accessing it after some while?
I hope the information above can be useful. If there is any update or I misunderstand you, please feel free to let me know. I will continue to assist you.
Your understanding and co-operation are highly appreciated.
Thanks for your precious time. Have a nice day!
Sincerely
Md Ashabul Haque | Microsoft Community Moderator