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/utils/logError.ts

@@ -0,0 +1,19 @@
+/**
+ * @file Frontend error logging utility that forwards errors to the backend telemetry service.
+ * @copyright nhcarrigan
+ * @license Naomi's Public License
+ * @author Naomi Carrigan
+ */
+/* eslint-disable no-console -- Errors are forwarded to backend via the overridden console.error */
+
+/**
+ * Logs an error to the backend telemetry service.
+ * Accepts the same arguments as console.error — conventionally a context string
+ * followed by the error value.
+ * @param logArguments - The values to log, forwarded directly to console.error.
+ */
+const logError = (...logArguments: Array<unknown>): void => {
+  console.error(...logArguments);
+};
+
+export { logError };

apps/web/src/utils/logger.ts

@@ -0,0 +1,68 @@
+/**
+ * @file Frontend logger that forwards console output to the backend telemetry service.
+ * @copyright nhcarrigan
+ * @license Naomi's Public License
+ * @author Naomi Carrigan
+ */
+/* eslint-disable no-console -- This file intentionally overrides console methods */
+
+type Level = "debug" | "info" | "warn";
+
+const post = (path: string, body: object): void => {
+  void fetch(path, {
+    body:    JSON.stringify(body),
+    // eslint-disable-next-line @typescript-eslint/naming-convention -- HTTP header names use kebab-case
+    headers: { "Content-Type": "application/json" },
+    method:  "POST",
+  }).catch(() => {
+    // Intentionally swallowed — we cannot log logger failures without infinite recursion.
+  });
+};
+
+/**
+ * Overrides the global console.log and console.error methods so that all
+ * frontend log output is forwarded to the backend telemetry endpoints.
+ * Must be called once at application startup before any other code runs.
+ */
+const initialiseFrontendLogger = (): void => {
+  const originalLog = console.log.bind(console);
+  const originalError = console.error.bind(console);
+
+  console.log = (...consoleArguments: Array<unknown>): void => {
+    originalLog(...consoleArguments);
+    const level: Level = "info";
+    const message = consoleArguments.map((argument) => {
+      return typeof argument === "string"
+        ? argument
+        : JSON.stringify(argument);
+    }).join(" ");
+    post("/api/fe/log", { level, message });
+  };
+
+  console.error = (...consoleArguments: Array<unknown>): void => {
+    originalError(...consoleArguments);
+    const message = consoleArguments.map((argument) => {
+      if (argument instanceof Error) {
+        return `${argument.message}\n${argument.stack ?? ""}`;
+      }
+      return typeof argument === "string"
+        ? argument
+        : JSON.stringify(argument);
+    }).join(" ");
+    const context = "console.error";
+    post("/api/fe/error", { context, message });
+  };
+
+  console.warn = (...consoleArguments: Array<unknown>): void => {
+    originalLog(...consoleArguments);
+    const level: Level = "warn";
+    const message = consoleArguments.map((argument) => {
+      return typeof argument === "string"
+        ? argument
+        : JSON.stringify(argument);
+    }).join(" ");
+    post("/api/fe/log", { level, message });
+  };
+};
+
+export { initialiseFrontendLogger };

apps/web/src/utils/notification.ts

@@ -4,6 +4,7 @@
  * @license Naomi's Public License
  * @author Naomi Carrigan
  */
+import { logError } from "./logError.js";
 
 /**
  * Requests browser notification permission from the user.
@@ -38,7 +39,8 @@ const sendNotification = (title: string, body: string): void => {
   try {
     // eslint-disable-next-line no-new -- Notification constructor has side effects
     new Notification(title, { body: body, icon: "/favicon.ico" });
-  } catch {
+  } catch (error_: unknown) {
+    logError("send_notification", error_);
     // Silently ignore — notifications may fail silently
   }
 };

apps/web/src/utils/sound.ts

@@ -4,6 +4,7 @@
  * @license Naomi's Public License
  * @author Naomi Carrigan
  */
+import { logError } from "./logError.js";
 
 type SoundEvent =
   | "achievement"
@@ -101,7 +102,8 @@ const playSound = (event: SoundEvent): void => {
       oscillator.start(startTime);
       oscillator.stop(endTime);
     }
-  } catch {
+  } catch (error_: unknown) {
+    logError("play_sound", error_);
     // Silently ignore — audio may not be available in all environments
   }
 };