feat: error handling, logging, analytics, OG tags, and sticky sidebar (#44)

## Summary

- Add comprehensive try/catch error handling across all API routes, middleware, and the Hono global error handler, piping every unhandled error to the `@nhcarrigan/logger` service to prevent silent crashes and unhandled Promise rejections
- Add a `logError` utility on the frontend that forwards errors through the overridden `console.error` to the backend telemetry endpoint; apply it to every silent `catch {}` block in the game context, sound, notification, and clipboard utilities, and wrap the React tree in an `ErrorBoundary`
- Add Plausible analytics, Open Graph + Twitter Card meta tags, Tree-Nation widget, and Google Ads to `index.html`
- Make the game sidebar sticky with a `--resource-bar-height` CSS custom property offset so it stays viewport-height without overlapping the resource bar; reset sticky behaviour in the mobile responsive override

## Test plan

- [ ] Lint passes: `pnpm lint`
- [ ] Build passes: `pnpm build`
- [ ] Verify errors thrown in API routes appear in the logger service rather than crashing the process
- [ ] Verify frontend errors appear in the `/api/fe/error` backend log
- [ ] Verify Open Graph tags render correctly when sharing the URL
- [ ] Verify Plausible analytics fires on page load
- [ ] Verify Tree-Nation badge renders in the sidebar
- [ ] Verify sidebar stays fixed while the main content scrolls on desktop
- [ ] Verify mobile layout is unaffected

✨ This issue was created with help from Hikari~ 🌸

Reviewed-on: #44
Co-authored-by: Hikari <hikari@nhcarrigan.com>
Co-committed-by: Hikari <hikari@nhcarrigan.com>

apps/web/src/styles.css

@@ -26,6 +26,7 @@
   --radius: 8px;
   --radius-lg: 12px;
   --font: "Segoe UI", system-ui, sans-serif;
+  --resource-bar-height: 3.5rem;
 }
 
 body {
@@ -136,6 +137,10 @@ body::before {
   flex-direction: column;
   align-items: center;
   gap: 1rem;
+  position: sticky;
+  top: var(--resource-bar-height);
+  height: calc(100vh - var(--resource-bar-height));
+  overflow-y: auto;
 }
 
 .game-content {
@@ -3181,8 +3186,11 @@ body::before {
     border-right: none;
     flex-direction: row;
     gap: 0.75rem;
+    height: auto;
     justify-content: center;
     padding: 0.5rem 0.75rem;
+    position: static;
+    top: auto;
     width: 100%;
   }