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/tps.svg

@@ -0,0 +1,15 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 48 48" fill="none">
+  <!-- "TPS Report Expert" - Clipboard with TPS -->
+  <!-- Clipboard board -->
+  <rect x="8" y="8" width="32" height="36" rx="2" fill="#78350f"/>
+  <!-- Clip -->
+  <rect x="16" y="4" width="16" height="8" rx="2" fill="#94a3b8"/>
+  <rect x="18" y="6" width="12" height="4" rx="1" fill="#cbd5e1"/>
+  <!-- Paper -->
+  <rect x="12" y="12" width="24" height="28" rx="1" fill="#f8fafc"/>
+  <!-- TPS text -->
+  <text x="24" y="24" font-size="10" fill="#1e293b" font-family="sans-serif" font-weight="bold" text-anchor="middle">TPS</text>
+  <rect x="14" y="28" width="20" height="2" rx="1" fill="#94a3b8"/>
+  <rect x="14" y="32" width="16" height="2" rx="1" fill="#94a3b8"/>
+  <rect x="14" y="36" width="18" height="2" rx="1" fill="#94a3b8"/>
+</svg>