Attempting offload of the App was (technically) the correct approach - but something has clearly gone wrong.
First, lets try to save/preserve the data that remains...
As for preserving the data, you need a backup. It may not be too late - and may already exist. I assume you son is using his “free” 5GB iCloud and that iCloud backup is already enabled? If not, do so now:
Settings > [Name / AppleID] > iCloud > iCloud Backup - set to ON
Settings > [Name / AppleID] > iCloud > Manage Storage > Backups > [This iPad] - scroll down the list of Apps, ensuring that App data for everything that needs to be included in the backup (such as Procreate) is included in the backup.
If these settings are already correct, good, you’re in a better place if the fault ultimately requires a system restore. If not already set-up, and the dataset still exists, it may be possible to save it.
If your Son’s Procreate art is valuable to you (or him), if the 5GB “free” allowance is insufficient, use a “paid” iCloud storage tier - if only as a temporary measure. You need to ensure that you always have a backup of anything that is important to you prior to having an unforeseen crisis or problem - this being applicable to both you and your son!
Now, lets try to resolve the App purchase and installation issue...
Does you son have more than one device - such as iPhone? If so, he might instead attempt making the Procreate App purchase from a device that doesn’t have the Procreate App/data; the only caveat is that he must obviously be signed-in to the Apple App Store with his own AppleID. This will hopefully work-around the problem.
Once the App is purchased against his the AppleID account, if should be downloadable to his iPad.
If this the App remain stubbornly out of reach, assuming the data is successfully backed-up, you can move onto more invasive measures to fix the problem. For now, I’ll leave it at that - and worry about other steps only if needed.
I hope this guidance proves to be helpful in resolving the problem. Please let us know how you get on.