Could you try performing the same action but with a curl command rather than via Postman, to rule out that this is being caused by something on Postman’s side? eg:
This command should send a PUT request to the Shopify API to update the SKU of the specified variant of the connected store, and if it works then it would be worth looking at how auth is set up on Postmans side.
If you’re still experiencing issues you may need to contact Partner Support who can take a deeper look into this call and any logs we can see on our end.