Is you Server Side synchronization not working and mailbox test failing in your environment even though all your configurations are correct? Double check your environment Background operations are not disabled.

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First of all, if your server side synchronization is not working for Production environment, then this blog may not help you. This only applies if your environment is in SandBox mode.
Now when an environment is in SandBox mode, you know you have the option of putting the environment in Administration mode. When put in Administration mode, only System Administrators or System Customizers will be able to sign in to the selected sandbox environment.
That’s fine. There is another option – “Background Operations” which you can keep enabled even when your environment is in Administration mode.

What will happen if you set Background operations to disabled?
As per Microsoft definition – “Select to disable all asynchronous operations such as workflows and synchronization with Exchange. Emails will not be sent and server-side synchronization for appointments, contacts, and tasks are disabled”
So when background operations are disabled, your server side sync and also operations like  testing and enabling mailboxes, shall not work. So next time you face an issue with server side sync or testing and enabling mailboxes, you can do a double check.
Before I end this, a quick side note. Even when your background operations are disabled, any custom code like Plugins and workflow assemblies still continue to work.
Hope this helps and saves you some time if you face an issue like this.
Debajit Dutta
(Microsoft MVP)