All my (downloaded?) files restored from Time Machine are marked as "damaged". I assume the problem is similar to this one: All downloaded files cannot be opened as they are 'damaged and should be moved to the Trash' so I try to change the "Allow app…" setting.
I open Security & Privacy and see App Store is selected:
I click the padlock and check "App Store and identified developers":
(I also notice that "Anywhere" is no longer an option.)
I leave System Preferences and try to open my files, but still get the error. So I go back to System Preferences, Security & Privacy and the old option is still selected:
Best Answer
Since this is a new Mac and nothing was working anyway, I decided I had nothing to lose by wiping it and starting over. So I restarted it and held down Command + R. From the menu I selected to reinstall macOS. After waiting 40 minutes I was disappointed to see that this option did not wipe the drive, and my restored accounts were still there on the login screen. I was about to restart again and this time format the drive, but I thought What the heck, and logged into my account. Surprisingly none of the files I opened were reported as damaged! Everything seems to be working now.