When you do a manual import using Outlook, the delay is expected since it takes a lot of time to sync (upload) 40GB into the mailbox. During that time, no new emails will arrive either since it is still processing the upload.
You can see the current sync status in the following way; What is Outlook synchronizing now?
As for the network upload method;
Is this to the same mailbox or a different one? Don't use the network upload and an Outlook import at the same time, especially with the same data or you'll end up with duplicates.
It is recommended to upload to the user's Online Archive instead of the user's active mailbox.
The error suggests an authentication error which is detailed further down in the log and not part of your screenshot.
That said, I don't see how an Azure Premium P1 license is relevant in this case either.