Add installable PWA and offline cache

[aliorhun]

Summary

Implements items 7–9 in one PWA-focused change set:

• add manifest.webmanifest with relative start_url / scope for GitHub Pages subpaths
• add 192×192 and 512×512 MathNote app icons, including maskable support
• register a service worker only on HTTP/HTTPS so direct file:// usage remains supported
• precache the generated application shell, bundle, styles, KaTeX fonts, manifest and icons
• use a content-derived cache version for each build
• remove stale MathNote caches when a new service worker activates
• provide offline navigation fallback to the cached app shell
• extend the existing offline verifier with PWA/manifest/service-worker checks
• document installable PWA behavior

GitHub Pages compatibility

All PWA URLs are relative (./...) so deployment works at:
https://alorak.github.io/mathnote/

The existing Pages workflow continues to publish dist/; the build now adds:

• manifest.webmanifest
• sw.js
• icons/icon-192.png
• icons/icon-512.png

Cache/update behavior

Each build hashes the generated distribution and creates a cache name such as:
mathnote-<content-hash>

On activation, older mathnote-* caches are deleted and the new service worker takes control.