Well, on my machine this folder weighs in at a whopping 0KB, so I don't think what you deleted was actually critical, although that doesn't explain why it stopped working for you.
The following command from an elevated powershell should reregister all the components that are failing:
Get-AppXPackage -AllUsers | Foreach
As for the logs, you should be able to find these in Event Viewer, under:
Applications and Services Logs\Microsoft\Windows\Apps\Microsoft-Windows-TWinUI/Operational event log.