I want to create a system where an automatic SLA is assigned to certain type of tasks (without the task creator marking a due date) and in case the SLA is mentioned less by the creator (Urgent requests) it goes for manager’s approval and is assigned to the actual assignee once supervisor approves.
Welcome, @Aishwarya_Gupta,
You should be able to accomplish these things with Rules provided you have Asana Business or Enterprise plan.
More info is at:
You may want to have either Sections or a single-select custom field that represent the stages the work goes through as you outlined it, and another single-select custom field for the types of tasks you have, including the type that you would want to go through this workflow. Your rules can reference both to target the tasks.
Hope that helps,
Larry