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Dear Anja MZH,
Thank you for coming back.
We are very sorry for the inconvenience this situation has caused you.
I found the same thing in my tests, when using the 16.64 version of the Office for Mac suite, I couldn't save files to the OneDrive side.
Currently, I recommend that you create a new file directly in the web version of OneDrive. At the same time, we take your feedback very seriously, and I think the development team of the product submitted this as well. Thanks for pointing out this phenomenon. At the same time, I also suggest that you can submit your feedback to the development team, I believe that this situation will be avoided after the new version is released.
More information for you to reference: How do I give feedback on Microsoft Office?
Sincerely,
Tin | Microsoft Community Moderator