You don't HAVE TO have a cookie banner for cookies which don't require consent.

Cookies not requiring consent :

  - "technical" cookies: for session, saving some user preferences (consenting to cookies or not, language etc.)
  - cookies used for load balancing or to protect against fraud
  - cookies used to save a cart or used to invoice some service
  - usage statistics cookies IF the data is anonymous

Also, the law is about trackers, not specifically cookies: so data in local and session storage are concerned as does browser fingerprinting.