When I choose the 'Move to' option for a file in SharePoint, then in addition to the file being moved to the SharePoint site of choice, the file is also moved to the recycle bin in OneDrive.

Is it possible to have a notification that this is actually happening?

Users are starting to panic when they notice their files in the recycle bin and when you're moving a few hundred files, it takes a long time to double check everything is there.