Can you explain in more detail to how the GDPR applies to unstructured forms? Would those be forms specifically for inputing personal data, or any free text at all?
If it contains personal data on an EU natural person regardless of where the company is based is based, or on any natural person anywhere if the company is EU based, it is subject to the GDPR.
If you're providing a storage service to a business that handles personal data, your a data processor, not a data controller.
If you're the data controller, you need a classification technology that can identify personal data in those documents (amongst other capabilities).
As always, there are exceptions, but that's the general rule.