The specific requirements are for users to take surveys unauthenticated which are related to an incident.
The requested behavior here is to both take a survey unauthenticated, and have it tied to an incident, the survey will need to be configured for and taken within service portal. There is a process that will need to be implemented in order for the requested behavior to be possible. The broad steps include creating a trigger condition, making a public survey, and setting up service portal to allow surveys. There is a very well documented Community blog about this process. Please see the link to this below:
Setting up public surveys in Service Portal