I'm on a Mac and I had a disk crash and had to restore from Time Machine. I now get messages about scratch disks being locked or unwritable. I can't even Save As. Help!

The original drive was named LaCie, as was the replacement drive (the system now sees the new drive as LaCIe 1). The new drive is APFS-formatted with a GUID Partition Map. It seems that I can save to a different folder, but I have no option for scratch disks other than the system drive, on which I’m storage space-challenged. Is there a way for me to update the existing app installations for permissions to reference the new drive?