Migrate to VitePress, drop lyticus, bump tooling to LTS

[botre]

Summary

• VuePress 1 → VitePress 1.6.4 — drops 124 of 127 npm audit findings (the remaining 3 are moderate dev-server-only esbuild advisories trickling through Vite, no production impact).
• Drop lyticus analytics dependency (no replacement wired in).
• Sentry: drop @sentry/browser + @sentry/integrations + @sentry/tracing v7 in favour of @sentry/vue v10 with the functional integrations API (browserTracingIntegration()).
• Tooling: prettier 2 → 3, husky 8 → 9, pretty-quick 3 → 4. Husky pre-commit no longer sources the deprecated _/husky.sh.
• Node LTS: .tool-versions pinned to Node 24 (Active LTS); CI uses actions/checkout@v6 + actions/setup-node@v6 with node-version: "24" and npm cache.
• Plugins: replaced vuepress-plugin-sitemap with VitePress's built-in sitemap config; replaced vuepress-plugin-robots with a static docs/public/robots.txt; dropped @vuepress/plugin-back-to-top (default theme already has it).
• Content: renamed docs/README.md → docs/index.md and docs/setup/README.md → docs/setup/index.md for VitePress home conventions; moved public assets from docs/.vuepress/public/ to docs/public/ and rewrote markdown image paths from ../.vuepress/public/X to /X.
• UI: enabled local search, widened the sidebar to match readability, sized the search button to match the legacy site (~240px), replaced the deprecated apple-mobile-web-app-capable meta with mobile-web-app-capable (kept the legacy one for older iOS Safari).
• Build/deploy: npm run build / npm run dev now invoke vitepress; the deploy script syncs from docs/.vitepress/dist.

Verification

• npm run build is green (~5s, sitemap generated).
• npm audit after the migration: 3 moderate (down from 127 — all dev-server esbuild only).
• Toured the local dev server and cross-checked against https://documentation.formspark.io/. Home, Slack integration page (with images), React example (with createRoot), and the new SvelteKit page all render with correct sidebar, navigation, and code highlighting.

Test plan

• Rebase / merge once Fix typos and refresh framework snippets #154 (typo + snippet refresh) lands — this branch was cut from master before that PR was open.
• Run npm run build in CI and confirm a green deployment.
• Visit the deployed site, confirm Sentry initialises in production and pages load with no console errors.
• Confirm documentation.formspark.io/sitemap.xml and /robots.txt resolve.