You don't need a banner if you use cookies. You only need a banner if you store data about a user's activity on your server. This is usually done using cookies, but the banners are neither specific to cookies nor inherently required for all cookies.

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Also: in general the banners are generally not required at all at an EU level (though some individual countries have implemented more narrow local rules related to banners). The EU regs only state that you need to facilitate informed consent in some form - how you do that in your UI is not specified. Most have chosen to do it via annoying banners, mostly due to misinformation about how narrow the regs are.