It isn't very clear what is happening here.
You have an old mac pro, but you were running Mojave - is that correct?
Nothing should happen if you just download Sierra, unless you started the upgrade.
is that what happened?
Can you boot into the recovery partition?
Because if you can, then you should be able to mount or access /Users and backup all the files from your /Users/username directory to a new drive (not the one used for Time Machine). Then if you can either re-install (whatever macOS you actually want), or recover from Time Machine, then it should be possible to get all those files back from that new drive.
I'm assuming you can re-download the applications that you might have installed since your last backup.
But it isn't really clear what OS you were running earlier.
What OS did you want to have running?
Where does Mojave come into this discussion?
Does your old hardware even support Sierra or Mojave?