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/api/src/routes/about.ts

@@ -7,6 +7,7 @@
 /* eslint-disable stylistic/max-len -- URL cannot be shortened */
 /* eslint-disable require-atomic-updates -- Simple cache; race condition is acceptable */
 import { Hono } from "hono";
+import { logger } from "../services/logger.js";
 import type { AboutResponse, GiteaRelease } from "@elysium/types";
 
 // eslint-disable-next-line capitalized-comments -- v8 ignore
@@ -46,12 +47,24 @@ const fetchReleases = async(): Promise<Array<GiteaRelease>> => {
 const aboutRouter = new Hono();
 
 aboutRouter.get("/", async(context) => {
-  const releases = await fetchReleases();
-  const body: AboutResponse = {
-    apiVersion,
-    releases,
-  };
-  return context.json(body);
+  try {
+    const releases = await fetchReleases();
+    const body: AboutResponse = {
+      apiVersion,
+      releases,
+    };
+    return context.json(body);
+  // eslint-disable-next-line capitalized-comments -- v8 ignore
+  /* v8 ignore next 9 -- @preserve */
+  } catch (error) {
+    void logger.error(
+      "about",
+      error instanceof Error
+        ? error
+        : new Error(String(error)),
+    );
+    return context.json({ error: "Internal server error" }, 500);
+  }
 });
 
 export { aboutRouter };