The ePrivacy Directive does mention cookies in its text, but it says "cookies or similar devices", so it clearly includes localStorage, which the 2002 text predates.

And there was NEVER a requirement for a "cookie banner" in its text. Consent under it can be given in any other way that are not as intrusive, but it was the industry who chose the stupid banner and invasive analytics. Also notice that under both GDPR and ePrivacy Directive, consent is not required for cookies/etc with a legitimate purpose. Examples of those have been given under the ePrivacy Directive from almost the beginning, but more explicitly in the "Opinion 04/2012 on Cookie Consent Exemption" which is from 2012 and predates cookie banners.

[1] Here's an example of asking for consent to store a cookie that doesn't involve a banner: https://www.williamgrant.com . It's in the age-check modal.