Kubernetes Kit actually logs the serialized session sizes in DEBUG and time in ms used.
c.v.k.s.s.SessionSerializer : Serialization of attributes [com.vaadin.flow.server.VaadinSession.springServlet, springServlet.lock, org.springframework.security.web.csrf.HttpSessionCsrfTokenRepository.CSRF_TOKEN, clusterKey] for session DEBUG-SERIALIZE-20BA4484065B09C386D1B5529FC239CE with distributed key abe3f89e-f887-417d-9e65-1825c21b39db_SOURCE:20BA4484065B09C386D1B5529FC239CE completed in 405ms (143678 bytes)
Leif added ticket to improve documentation about this: Document Kubernetes Kit session size logging · Issue #4743 · vaadin/docs · GitHub