fix: PWA icons, SW method guard, start script

public/sw.js

@@ -74,6 +74,11 @@ self.addEventListener('fetch', (event) => {
   // Same-origin only
   if (url.origin !== self.location.origin) return;
 
+  // Only cache GET/HEAD — POST/PUT/DELETE/OPTIONS can't use Cache API
+  if (request.method !== 'GET' && request.method !== 'HEAD') {
+    return; // pass through, no caching
+  }
+
   // 1. Static assets → cache-first
   if (isStaticAsset(url)) {
     event.respondWith(cacheFirst(request, STATIC_CACHE));