A group of Microsoft Products and technologies used for sharing and managing content, knowledge, and applications.
Hello,
If the shared folder link has edit permission, the accessed user can see the Upload option like below:
But as you mentioned "we have other files within that folder which could have been uploaded by other customers. We do not want users to see those files", per my experience it's not possible to achieve it when you are sharing the link to the users.
In this situation, as a workaround, you can create a new folder in your OneDrive for Business and create a Request files link for the created folder to share it with the users. Once the users upload the files, you can move those files to your SharePoint site as per your requirement*.*
Reference: Create a file request (microsoft.com)
Thanks for understanding and stay safe!!
Best Regards,
Chitrahaas