[WebUI] PWA cold start shows a long blank screen before first paint

Bug Description

Cold starting the installed PWA (first open, or after the app is evicted and relaunched) shows a blank screen for a noticeable amount of time before anything renders. Launching from the home screen icon feels slower than opening the same page in Safari.

Steps to Reproduce

1. Install the WebUI to the home screen on iOS, and on Android for comparison.
2. Force-quit the app, then relaunch it from the home screen icon.
3. Observe the blank screen before the app shell paints.

Expected Behavior

Launch should paint the app shell promptly, following the iOS and Android PWA conventions:

• iOS should show a launch screen via apple-touch-startup-image instead of a blank surface while the web content loads.
• The app shell should be able to paint from cache on launch instead of waiting for a network round trip.

Additional Context

Client: iPhone Air, iOS 27, standalone PWA, self-hosted deployment over HTTPS.

Two concrete causes, both verified in the current tree:

1. No iOS launch screen is served. webui/index.html has no apple-touch-startup-image link and no launch screens are shipped, so iOS has nothing to display during launch and shows a blank screen.
2. The service worker serves the app shell network-first. In webui/public/sw.js, / is listed in NETWORK_FIRST_STATIC_PATHS, and the navigation path is fetch(request) with a cache fallback only when the network fails. First paint therefore depends on network latency on every cold start even when a valid cached shell exists, which is the worst case on a high-latency or restricted link. A stale-while-revalidate path for the shell would paint immediately and still pick up updates in the background.

Note that a shell is precached in PRECACHE (/, /manifest.json, /asset-manifest.json), so the cached copy exists but is not used on the fast path.

The inline boot splash in webui/index.html (.boot-splash) only appears after the document is parsed, so it cannot cover the native launch gap described in (1).