Install and configure Vercel Web Analytics - #1

Implemented Vercel Web Analytics for PetroBrain Web

## What was implemented

Successfully installed and configured Vercel Web Analytics following the latest official documentation from https://vercel.com/docs/analytics/quickstart.

### Changes made:

1. **Installed @vercel/analytics package**
   - Added `@vercel/analytics` version 2.0.1 to project dependencies
   - Used npm (the project's package manager) to install the package
   - Updated package.json and package-lock.json accordingly

2. **Configured Analytics in root layout**
   - Modified `app/layout.tsx` to import the Analytics component from `@vercel/analytics/next`
   - Added the `<Analytics />` component to the root layout body, alongside the existing Plausible analytics component
   - Followed Next.js App Router best practices by placing it in the root layout for app-wide analytics tracking

### Implementation details:

- **Framework**: Next.js with App Router (identified from project structure)
- **Installation method**: Framework-specific integration for Next.js as specified in Vercel documentation
- **Placement**: Added to `app/layout.tsx` root layout to ensure analytics tracks all pages
- **Compatibility**: Preserved existing analytics setup (Plausible) - both analytics solutions now run in parallel

### Verification:

✅ Package installed successfully via npm
✅ Linter passes with no errors
✅ Code follows existing project patterns and conventions
✅ Lock file updated correctly

### Notes:

- The Analytics component will automatically collect page view data once the app is deployed to Vercel
- Analytics must be enabled in the Vercel dashboard for the project to start collecting data
- The component gracefully handles development vs production environments
- Build verification showed a pre-existing configuration issue (missing NEON_AUTH_COOKIE_SECRET) unrelated to these changes
- All changes follow the official Vercel documentation retrieved on June 21, 2026

### Files modified:

- `app/layout.tsx` - Added Analytics import and component
- `package.json` - Added @vercel/analytics dependency
- `package-lock.json` - Updated with new package resolution

Co-authored-by: Vercel <vercel[bot]@users.noreply.github.com>