Hi Jac,
Thank you for connecting with us in Microsoft community.
According to your description, looks like you have already performed all the possible troubleshooting steps for making changes in your affected shared mailbox", this scenario is also happening after rebuilding the profile and on Outlook web application.
For this given scenario, I have consulted your case with my team member, I would like to share more specific information with you, now your current situation should be diagnosed by Microsoft's frontline support team by colleting some advanced logs information. Frontline technical support engineer can also involve specific support team for further analysis some particular situation if it is required.
Because to analysis your mentioned issue, certain logs will be required for technical support team, and this logs information will be collected from Office 365 global admin person via standard process.
For example: if something wrong between email account and server in your Office 365 Business tenant or some other reason etc.., this kind of information need to diagnose by technical support team from their backend resources and permission.
Since we forum moderators have limited permissions and access resources, due to this reason and for data privacy of users, we are unable to collect certain kind of logs information in the public forum which contain sensitive information.
After diagnosing the scenario, our technical support team can provide possible information from their end.
For the above provided standard process information, in your organization, Office 365 global admin person may need to contact Office 365 support team on backend via an open service request so they can diagnose this specific scenario through some more technical resources and escalation process.
For this standard process, here's the official document for the global admin reference: Get support - Microsoft 365 admin | Microsoft Learn (Online Option).
End users need to contact Office 365 global admin person in their organization to do some standard process and to connect with frontline technical support team.
Important note: If any organization's Office 365 Business/Business/Education subscription is from a syndicated partner or reseller, and if the global admin can't open the service request on their end, they may need to contact the reseller's support provider so they can help the global admin to open the service request on their end. after the Office 365 support team will involve in the created service request.
I am really appreciating your valuable cooperation.
Have good day.
Sincerely
Vaidya Darpan
