feat(offline): hold through a short network drop with a caching worker

The service worker did Web Push and nothing else, with a note that a cache
serving yesterday's data was worse than an honest "cannot connect". This adds a
cache that does not do that: network-first for everything that can go stale, so a
reader online always gets the live answer and the cache is reached only when the
network cannot answer. The task and note lists stay live; they just no longer go
blank the moment the signal does — a reload through a tunnel, a lift or a
base-station handover comes back to the app instead of the browser's offline page.

Writes are untouched and still go straight to the network; api.js already retries
them across the same short drop. The shell cache is versioned so a deploy lands in
a fresh cache and the old one is dropped on activate; the data cache is cleared on
sign-out so the next person on the browser does not inherit it.

The old hand-registered /sw.js becomes SvelteKit's src/service-worker.js, which it
registers itself, and the push handlers move across unchanged.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

web/src/lib/push.js

@@ -26,9 +26,13 @@ export function permission() {
 }
 
 async function registration() {
-	// `ready` waits for an active worker; register() alone resolves while the
-	// worker is still installing, and subscribing against that fails.
-	await navigator.serviceWorker.register('/sw.js');
+	// SvelteKit registers src/service-worker.js itself on load, so normally there
+	// is already a registration here. Register it by hand only if there is not yet
+	// one — a push subscribe that races the app's own registration would otherwise
+	// find nothing. `ready` waits for an active worker; register() alone resolves
+	// while the worker is still installing, and subscribing against that fails.
+	const existing = await navigator.serviceWorker.getRegistration();
+	if (!existing) await navigator.serviceWorker.register('/service-worker.js');
 	return navigator.serviceWorker.ready;
 }