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/index.ts

@@ -7,22 +7,24 @@
 import { serve } from "@hono/node-server";
 import { Hono } from "hono";
 import { cors } from "hono/cors";
-import { logger } from "hono/logger";
+import { logger as honoLogger } from "hono/logger";
 import { aboutRouter } from "./routes/about.js";
 import { apotheosisRouter } from "./routes/apotheosis.js";
 import { authRouter } from "./routes/auth.js";
 import { bossRouter } from "./routes/boss.js";
 import { craftRouter } from "./routes/craft.js";
 import { exploreRouter } from "./routes/explore.js";
+import { frontendRouter } from "./routes/frontend.js";
 import { gameRouter } from "./routes/game.js";
 import { leaderboardRouter } from "./routes/leaderboards.js";
 import { prestigeRouter } from "./routes/prestige.js";
 import { profileRouter } from "./routes/profile.js";
 import { transcendenceRouter } from "./routes/transcendence.js";
+import { logger } from "./services/logger.js";
 
 const app = new Hono();
 
-app.use("*", logger());
+app.use("*", honoLogger());
 app.use(
   "*",
   cors({
@@ -33,6 +35,7 @@ app.use(
 );
 
 app.route("/about", aboutRouter);
+app.route("/fe", frontendRouter);
 app.route("/auth", authRouter);
 app.route("/game", gameRouter);
 app.route("/boss", bossRouter);
@@ -48,8 +51,27 @@ app.get("/health", (context) => {
   return context.json({ status: "ok" });
 });
 
+app.onError((error, context) => {
+  void logger.error(
+    "hono_unhandled_error",
+    error instanceof Error
+      ? error
+      : new Error(String(error)),
+  );
+  return context.json({ error: "Internal server error" }, 500);
+});
+
 const port = Number(process.env.PORT ?? 3001);
 
-serve({ fetch: app.fetch, port: port }, () => {
-  process.stdout.write(`Elysium API running on port ${String(port)}\n`);
-});
+try {
+  serve({ fetch: app.fetch, port: port }, () => {
+    process.stdout.write(`Elysium API running on port ${String(port)}\n`);
+  });
+} catch (error) {
+  void logger.error(
+    "server_startup",
+    error instanceof Error
+      ? error
+      : new Error(String(error)),
+  );
+}