Oh dear! It seems you have more corruption than you first thought.
Assuming you are running the latest free upgrade FH v6.2.7 then Snapshots are an integral feature of Projects.
( When you installed FH v6 on your new laptop did you update to that latest free version? )
However, Snapshots are only created when you open a Project and no more than once per day.
It is very strange that none of your Projects have any Snapshot commands.
Your one-name study is no longer being recognised as a Project, but only as a standalone GEDCOM.
The top line of the main FH window says - Family Historian Gedcom - instead of - Family Historian Project – and it is not listed in the Projects Window.
That explains the greyed-out Backup commands that are only available for Projects.
Without a detailed listing of the folders and files inside My Documents\Family Historian Projects\ for your one-name study it is difficult to advise what needs fixing.
Unfortunately, it is tedious to attach screenshots to these Emails because we must wait for an administrator to review them before they are passed on.
However, you are certain that your GEDCOM data is compromised so fixing the files to restore it as a Project is pointless.
Without Snapshots the only option is to use your most recent Backup. Remind me, is that a GEDCOM Only or a Full Backup?
If GEDCOM Only then you will need to create an empty Project into which to restore the GEDCOM backup.
Then you must copy or move all the Media from the broken ‘Project’ Media folder to the new Project Media folder.
Do you know where that Media folder exists inside the Project folder structure?