Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Dear Max Staniland,
The detailed steps would be following (if you want to move files from one SharePoint site to another new SharePoint site):
1.Create the new site, then sync one document library from the new site to your local computer. (this is destination library)
2.Go to your old SharePoint site which contains files you want to move, find the document library and sync files to local computer*(this is source library)*
3.In File explorer, move files from source folder to destination folder.
(As far as we know, when we move files in File explorer, it may display the progress bar to show you the transferring status)
After you move files to the destination folder, OneDrive will sync these files to SharePoint Online, as long as it doesn't display any sync error, your files will all sync to SharePoint Online. When it finishes synchronization, you can go to SharePoint Online, go to the new SharePoint site and check the result.
If you want other people see the transferred files in the new SharePoint site, just let them access the new SharePoint site in SharePoint Online on their devices.
For your concern about "how would you find out what has been missed and what hasn't in the transfer"
In the destination folder if you find all files show syncing status icon (blue cloud icon, or green tick icons), they should have been synced to SharePoint Online.
If you find files shows red X icon, it may have sync issue and cannot sync to SharePoint Online, then it isn't transferred to the new SharePoint site. In this situation, you can also try manually uploading that file to SharePoint Online.
For reference: What do the OneDrive icons mean? (microsoft.com)
Hope above can help you!
Sincerely,
Tina | Microsoft Community Moderator