Could you try navigating to cognitive service page do a role assignment to ACS resource, using below steps-
Add role from Cognitive Services Azure Portal page
Navigate to the portal page for the cognitive service.
Select the “Access control (IAM)” tab.
Click the “+ Add” button.
Select “Add role assignment” from the pop-up menu.
Choose the “Cognitive Services User” role to assign, then click “Next.”
• Choose the “Managed Identity” option for “Assign access to.” Then press “+ Select members.” This will cause the “Select managed identities” flyout to appear.
• Choose your subscription from the “Subscriptions” drop down menu.
• Select “System-assigned managed identity.” This should cause the list of your system assigned identities to appear below in a list.
• Select the identity from the list and press the “select” button at the bottom of the flyout. This will add the selected identity to the list of members on the “Add role assignment” page.
• Click “Review + assign” when you have selected all the identities you wish to add the role to.
• Click “Assign” on the following page. This will assign the role to the managed identity.
Let us know how it goes.