A Microsoft file hosting and synchronization service.
Thank you.
While right click and selecting 'Always keep on this device' doesn't do anything, the grey icons to the right of each file/folder work sometimes. Some of them need to be clicked several times.
Surprisingly, it did not download almost anything from the cloud.
But it somehow connected files and folders in OneDrive location to files that exist in OneDrive catch location /Users/YOUR_USER_NAME/Library/Group Containers/UBF8T346G9.OneDriveStandaloneSuite/OneDrive.noindex/OneDrive