How the fuck does TypeScript still not have service worker support? Seriously, it's just a typings file. People have written that typings file. They would just have to include it in the lib collection shipped with the compiler. Yeah, it would have DOM calls intermixed with the SW api, but frankly, having the typings for a set of calls you can't use is infinitely better than missing them for a set of calls you can.
The relevant issue is 5 years old btw.