I notice that Chrome puts service workers, indexed databases and local/session storage under "cookies" in the site info dropdown. Are these things in any way considered ways to access personal information or uniquely identify and track a visitor as per GDPR scope? Or is it at least theoretically possible to do so?
I am not a lawyer nor do I reside in the EU, but to the best of my understanding GDPR is a law about user tracking, not a law about which browser APIs you can use. In the eyes of the law it doesn't matter whether the Service Worker API is able to be used to uniquely identify and track a visitor - the law only cares about whether you actually use the API to do so.
So yes, Service Workers are theoretically possible to track users with. But if you're using them in a way that doesn't result in user-tracking, then no worries. Again, AFAIK.
Let me make it more simple for you. GDPR means that you're handling the data of people in Europe. Whenever a user comes on your website, the website stores a small amount of data (also known as Cookies), and when your website is storing that small amount of data, then you have to declare it by law, and that is GDPR.
No matter what kind of website or business you own but if you have European audience, you must have to add GDPR consent.
Even if you're not using Google Analytics or any other Tracking plugin but your CMS (Wordpress, Joomla etc) will keep some data from your visitors. So it's a must for you to have GDPR.