Can I block access to the user’s own account’s Google Drive, while still allowing them to collaborate on other shared folders/etc?

We are a completely MS organization, but we sometimes have to work with other organizations and some of those organizations prefer to use Google Workspace. They will add us to shared folders, shared Google Docs, and so on, for us to upload and edit. (eg, if a client asks us to send them product data and gives us a folder to add it to… if possible we try to be cooperative with their preferences)

We have set up Cloud Identity Free for our organization for this purpose.

We want to allow users to only be able to upload to those shared drives they have been added to, but their own Google Drive should remain empty (they should be using their OneDrive account if they need cloud storage). I have tried adding a storage limitation of 0GB but it doesn’t seem to apply to free accounts.

Is this possible?