Is there a way to restrict an native file browser to restrict access to OneDrive?
Are you working with a fully managed device or a work profile?
Even if you find options to disable specific file browser applications it is unlikely that you would be able to fully disable the functionality from inside applications.
If Microsoft Intune licenses are available to you I would consider looking at App protection policies overview - Microsoft Intune | Microsoft Docs, this will at least give you some control over data inside supported applications but may not be exactly what you are looking for.
Feel free to provide more information around the specific use case.