I would love to learn about your plans for Service Worker support for the API.
Topic on Talk:Wikimedia REST API
The REST API is primarily targeted at serving the data consumed by increasingly fatter clients, including those taking advantage of ServiceWorkers.
We are also looking into leveraging ServiceWorkers to improve performance and offline support. As part of this effort, we have done some research and prototyping into a) a node environment for running unmodified serviceworker code on behalf of older clients, and b) streaming HTML transformation / composition tooling. We do intend to develop a PWA targeted at mobile web over the next 12 months which might use some of this research, but expect this PWA to be limited to an opt-in beta feature until at least mid 2018.