Add Vercel Analytics and Speed Insights

[socialawy]

Problem

No visibility into app usage or performance metrics. We need basic monitoring to understand how the app is being used and identify performance bottlenecks.

Solution

Integrate Vercel's built-in Analytics and Speed Insights packages.

Tasks

• Install @vercel/analytics and @vercel/speed-insights
• Add <Analytics /> component to the root layout (app/layout.tsx)
• Add <SpeedInsights /> component to the root layout (app/layout.tsx)
• Only load in production (check NODE_ENV or use Vercel's built-in environment detection)
• No additional user tracking or cookies beyond what Vercel provides by default
• Verify no impact on dev mode performance or console warnings

Acceptance Criteria

• @vercel/analytics and @vercel/speed-insights are installed as dependencies
• Both components are rendered in the root layout
• Analytics data appears in the Vercel dashboard after a production deploy
• Speed Insights data appears in the Vercel dashboard after a production deploy
• No analytics scripts loaded in development mode
• No impact on dev mode performance or build size concerns
• No new cookies or tracking beyond Vercel defaults

Context

• Stack: Next.js 15 + React 19
• Hosting: Vercel
• Docs: Vercel Analytics, Speed Insights
• Live: https://tiny-museum-iota.vercel.app