Add flair badge gamification system with custom SVG badges

- Create 12 Office Space themed SVG badges (extraction, basement, printer,
  coffee, tps, bobs, memo, oface, stapler, conclusions, spreadsheet, flair-badge)
- Implement FlairBadge.astro component with localStorage persistence
- Add 15-second timer per page to earn flair
- Create floating counter, modal flair board, toast notifications
- Override Starlight Footer to inject flair system globally
- Add name capture dialog on first flair earned

Features:
- Badges glow golden when earned, grayscale when locked
- Progress persists across browser sessions
- Stan quote: "We need to talk about your document processing..."

public/flair/conclusions.svg

@@ -0,0 +1,17 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 48 48" fill="none">
+  <!-- "Jump to Conclusions" - The Jump to Conclusions mat -->
+  <!-- Mat base -->
+  <rect x="4" y="28" width="40" height="16" rx="2" fill="#16a34a" transform="skewX(-5)"/>
+  <rect x="6" y="30" width="36" height="12" rx="1" fill="#22c55e" transform="skewX(-5)"/>
+  <!-- Conclusion squares -->
+  <rect x="8" y="32" width="8" height="8" rx="1" fill="#f8fafc" transform="skewX(-5)"/>
+  <rect x="18" y="32" width="8" height="8" rx="1" fill="#fef08a" transform="skewX(-5)"/>
+  <rect x="28" y="32" width="8" height="8" rx="1" fill="#fca5a5" transform="skewX(-5)"/>
+  <!-- Jumping figure -->
+  <circle cx="24" cy="12" r="5" fill="#1e293b"/>
+  <path d="M24 17 L24 24" stroke="#1e293b" stroke-width="2" stroke-linecap="round"/>
+  <path d="M24 19 L18 22" stroke="#1e293b" stroke-width="2" stroke-linecap="round"/>
+  <path d="M24 19 L30 22" stroke="#1e293b" stroke-width="2" stroke-linecap="round"/>
+  <path d="M24 24 L20 30" stroke="#1e293b" stroke-width="2" stroke-linecap="round"/>
+  <path d="M24 24 L28 30" stroke="#1e293b" stroke-width="2" stroke-linecap="round"/>
+</svg>