Writing to lakehouse in different workspace using Notebook

I have 2 workspaces -

1 is development - To which all the developers have contributor / member access.

2 is Bronze Workspace - The developers don't have access to the workspace but I have provided them all permissions on the Lakehouse level, PFA The screenshot

The Devs can read the data present in the lakehouse (2nd Workspace) but when the developers try to write to it using spark notebook it gives the following error-

"Failure happened on 'destination' side. ErrorCode=LakehouseForbiddenError,'Type=Microsoft.DataTransfer.Common.Shared.HybridDeliveryException,
Message=Lakehouse failed for forbidden which may be caused by user account or service principal doesn't have enough permission to access Lakehouse. 

ErrorCode: 'Forbidden'. Message: 'Forbidden'. TimeStamp: 'Mon, 10 Jun 2024 08:14:47 GMT'..,Source=Microsoft.DataTransfer.ClientLibrary,
''Type=Microsoft.DataTransfer.Common.Shared.HybridDeliveryException,Message=Operation returned an invalid status code 'Forbidden',Source=,
''Type=Microsoft.Azure.Storage.Data.Models.ErrorSchemaException,Message=Operation returned an invalid status code 'Forbidden',Source=Microsoft.DataTransfer.ClientLibrary,'"

I know if i give them the access on the workspace level they can write to the Lakehouse present in the 2nd workspace but I want the devs to only have access to the specific Lakehouse and not the full access to these other workspaces.

Is there any way I can solve this?