@Laimis Thanks for the question. Can you please add more details about the steps that you performed and compute cluster details to check.
Can you please confirm are you using the AML Studio Designer to train the model?
Is the AML storage account restricts access to specific VNETs and the Compute Cluster isn’t in that VNET?
Also please confirm did you change your Default storage account key?
You can Update storage account key with below command.
Change storage account access keys - Azure Machine Learning | Microsoft Learn
az ml workspace sync-keys -w myworkspace -g myresourcegroup