Hi David,
Sorry for all the inconveniences it may have caused on your side.
Based on the description, it seems like there have something wrong with the files you try to move from Files app on iPad to OneDrive storage space. If my understanding is correct, may I know if the issue will start to happen when you click Copy button in the process below? If this is not the step on your side, kindly share us some more detailed screenshots so that we can test if the same issue will happen on our side.

Also, based on the error message you shared, it seems like it is from Files app side, kindly check Files App: Couldn't Communicate with a he… - Apple Community. Hence, you can have a try to sign-out and sign-in your Microsoft account again to check if it will show any differences. If the issue persists, try to reset OneDrive: Reset OneDrive (microsoft.com).
Besides, may I know if you are using a personal account or a school/work account in OneDrive that encountered with the issue?
Best Regards,
Mia