Draw a clean play/pause on the drop and make the app installable

The raised icon was cut into a mesh too coarse for its edges and did not line up
with the icon painted over it, so it came out doubled and jagged, and melting one
shape into the other went through blobby in-betweens. The icon is now only painted:
crisp and white on a dark disc like the page's round buttons, still turning with the
drop, and pause and play fade into each other as the new one grows in.

Some browsers only offer to install an app with a service worker. A minimal one at
/sw.js (served from the root so it covers the whole app) caches nothing and only
shows a short offline note instead of the browser's error page. The manifest gets
an id.

backend/src/http/mod.rs

@@ -294,6 +294,11 @@ async fn static_route(Path(path): Path<String>) -> Response {
     static_file(&path)
 }
 
+/// The service worker, at the root so its scope covers the whole app.
+async fn service_worker() -> Response {
+    static_file("sw.js")
+}
+
 async fn healthz() -> Response {
     (no_store(), Json(json!({ "ok": true }))).into_response()
 }
@@ -305,6 +310,7 @@ pub fn router(app: Arc<App>) -> Router {
     Router::new()
         .route("/", get(index))
         .route("/static/{*path}", get(static_route))
+        .route("/sw.js", get(service_worker))
         .route("/healthz", get(healthz))
         .route("/impressum", get(legal::impressum))
         .route("/datenschutz", get(legal::datenschutz))