I haven't found a clear answer to this but from my experiments the following appears true:
Service workers have no access to or control over the traditional browser cache. Is this intended? Are there ways to do this that I haven't discovered yet?
When I say "browser cache" I don't mean the CacheStorage API. I do know that the service worker has full access to the CacheStorage API. I mean the cache which is used when requests in the network tab of browser dev tools say "from memory cache" as opposed to "from service worker" or just straight up from an actual network request.