The theme-color meta tag is used to specify a toolbar color on Android. The color is used both in Chrome and when the page is used as a web app added to the home screen (actually, there is also a theme-color attribute in the manifest).
To turn the page into a web app (instead of a Chrome tab), add a web app manifest file. See https://developers.google.com/web/fundamentals/engage-and-retain/app-install-banners/ for some detail. Note that the service worker is not necessary for the web app look.
The service-worker is used to implement the off-line behavior of the app, but also web push notifications.