API Permission error: Access denied to read task template list in CCP Softphone for an agent

Hello, as we use an extended CCP with Softphone embedded via the IFRAME, we face an issue, that agents, who open the task creation page in Softphone get an error, that shows : We have one Task template configured and the agent_log says :

{
        "component": "ccp",
        "level": "ERROR",
        "text": "Failed to load list of task templates",
        "time": "2022-10-19T04:53:13.894Z",
        "exception": "null",
        "objects": "[\"{\\\"message\\\":\\\"Missing auth cookie. Please sign in.\\\",\\\"status\\\":401}\"]",
        "line": 60,
        "agentResourceId": "xxxxxxxxxxx",
        "loggerId": "xxxxxxxxxxxx"
    },
    {
        "component": "ccp",
        "level": "ERROR",
        "text": "'listTaskTemplates' API request failed",
        "time": "2022-10-19T04:53:13.893Z",
        "exception": {
            "type": "[object Object]",
            "message": "Missing auth cookie. Please sign in.",
            "stack": []
        },
        "objects": [
            {
                "request": {
                    "event": "api_request",
                    "requestId": "xxxxxxxxxx",
                    "method": "listTaskTemplates",
                    "params": {
                        "instanceId": "xxxxxxxxxxxxxx",
                        "queryParams": {
                            "status": "ACTIVE"
                        }
                    }
                },
                "response": {
                    "event": "api_response",
                    "requestId": "xxxxxxxxxx",
                    "err": "{\"message\":\"Missing auth cookie. Please sign in.\",\"status\":401}"
                }
            }
        ],
        "line": 61,
        "agentResourceId": "xxxxxxxx",
        "loggerId": "xxxxxxxxx"
    },

The current agent has the security profile "agent" assigned and get this errors. Another agent, not from the same network or site, and with security profile "Call center manager and admin" does not have the problems facing the other agents. In the security profiles there is a section Routing -> Task templates. For agent, it is empty. Could it be the case, that here the security profile needs at least the "view" permission to listTaskTemplates in the cCP frontend. It is confusing for me, which user needs which permission or setting to be able to use this task template dropdown in the frontend? Best regards Alex