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/coffee.svg

@@ -0,0 +1,14 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 48 48" fill="none">
+  <!-- "Case of the Mondays" - Coffee mug with steam -->
+  <!-- Mug body -->
+  <rect x="10" y="18" width="22" height="22" rx="3" fill="#78350f"/>
+  <rect x="12" y="20" width="18" height="18" rx="2" fill="#92400e"/>
+  <!-- Coffee surface -->
+  <ellipse cx="21" cy="22" rx="8" ry="2" fill="#451a03"/>
+  <!-- Mug handle -->
+  <path d="M32 22 Q40 22 40 30 Q40 38 32 38" stroke="#78350f" stroke-width="4" fill="none"/>
+  <!-- Steam wisps -->
+  <path d="M14 14 Q16 10 14 6" stroke="#94a3b8" stroke-width="2" fill="none" stroke-linecap="round"/>
+  <path d="M21 12 Q23 8 21 4" stroke="#94a3b8" stroke-width="2" fill="none" stroke-linecap="round"/>
+  <path d="M28 14 Q30 10 28 6" stroke="#94a3b8" stroke-width="2" fill="none" stroke-linecap="round"/>
+</svg>