Great question, and this is a classic Prod vs Dev mismatch issue. Here's what's likely going on and how to fix it:
Why it works in Dev but not Prod
The "Root folder not found" error usually means the base SharePoint folder for that entity (Cases in your situation) hasn't been initialized in the Prod environment yet. In Dynamics 365, the root folder for an entity is only created the first time someone opens the Documents tab on a record manually. If no one has done that in Prod, the root doesn't exist yet and your flow fails trying to build on top of it.
How to fix it
Manually initialize the root folder - Open any Case record in Prod, click the Documents tab, and let Dynamics 365 create the base folder in SharePoint. Do this once and it sets up the root for all Cases going forward.
Check your SharePoint Document Management settings in Prod - Go to Settings > Document Management > Document Management Settings and make sure Cases is enabled and pointing to the correct SharePoint site and library in Prod, not Dev.
Verify the Parent Site/Location record exists - Your flow likely references a Document Location record as the parent. That record exists in Dev but may not have been created in Prod. Check in Dynamics 365 under Document Locations and confirm the root location for Cases is there.
Check SharePoint library structure - Make sure the Cases folder/library actually exists on the Prod SharePoint site. If the flow was set up by copying from Dev, the library path might resolve correctly in Dev but be missing in Prod.
Best practice going forward
After setting up Document Management for a new entity in any environment, always open one record manually first and click Documents. This seeds the root folder and prevents this exact error before any automated flows run.