Is application-cookie based session persistence supported?

Need to know if there is support for application cookie stickiness or session persistence.

I went through the documentation for session persistence, I see that there are two types of session persistence supported. Refer - https://www.envoyproxy.io/docs/envoy/v1.34.0/api-v3/config/http/stateful_session
1. Cookie based session persistence
2. Header based session persistence

My requirement is to support session persistence only when the backend server sends a Set-Cookie in its response header. Only then the cookie should be set in the response and from then onwards, the session persistence should start. With current cookie-based session persistence, Envoy will add cookie from the first request itself. But it should add the cookie only when backend server sends a set-cookie in its response header.

Is this supported in Envoy?