A Microsoft file hosting and synchronization service.
Dear respected,
I went through your post carefully and it seems like you want to make sure that every tenant user will be able to collaborate together on organized folders and ensure that everyone can save and edit files directly within the shared folders from OneDrive space. If my understanding is correct, firstly, to make sure I can help on troubleshoot the error you and your members are facing on your side, please provide some more detailed screenshots for a better understanding and also, I need to simulate the same test environment to locate the root cause.
Meanwhile, another thing I want to share with you that might can provide a much better user experience based on the requirement within your organization is that using a SharePoint site Document library. It will be really easy to collaborate with folders and files, with the same permission setup just like OneDrive, even, the library can also be synced into local OneDrive sync client just like their own OneDrive contents. And everyone can work on the same file at the same time.
For more detailed information, below are some official article I found for you to have a reference:
Should I save files to OneDrive or SharePoint? - Microsoft Support
What is a document library? - Microsoft Support
Work with files in a document library - Microsoft Support
However, if you have already considered with SharePoint before and still OneDrive shared folder is more suitable for your scenario, then to troubleshoot the error you and your members are facing with regarding to "they still can't save a file directly to folders" and "an error saying we don't have proper permissions", any screenshots would be highly appreciated!
Please correct me if I made any misunderstanding and I will be here waiting for your updates to offer any further support.
Appreciate your time and patience. Hope you a nice day and stay safe!
Best Regards,
Mia