feat: initial prototype — core game systems (#30)

## Summary

This PR represents the full v1 prototype, implementing the core game systems for Elysium.

- Full idle/clicker RPG loop: resource collection, crafting, boss fights, exploration, and quests
- Adventurer hiring with batch size selector and progressive tier cost scaling
- Prestige, transcendence, and apotheosis systems with auto-prestige support
- Character sheet, titles, leaderboards, companion system, and daily login bonuses
- Auto-quest and auto-boss toggles
- Discord webhook notifications on prestige/transcendence/apotheosis
- Discord role awarded on apotheosis
- Responsive design and overarching story/lore system
- In-game sound effects and browser notifications for key events
- Support link button in the resource bar
- Full test coverage (100% on `apps/api` and `packages/types`)
- CI pipeline: lint → build → test

## Closes

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Closes #29

✨ This issue was created with help from Hikari~ 🌸

Co-authored-by: Naomi Carrigan <commits@nhcarrigan.com>
Reviewed-on: #30
Co-authored-by: Hikari <hikari@nhcarrigan.com>
Co-committed-by: Hikari <hikari@nhcarrigan.com>

apps/web/src/main.tsx

@@ -0,0 +1,23 @@
+/**
+ * @file Application entry point.
+ * @copyright nhcarrigan
+ * @license Naomi's Public License
+ * @author Naomi Carrigan
+ */
+/* eslint-disable import/no-unassigned-import -- CSS import has no exports to assign */
+import { StrictMode } from "react";
+import { createRoot } from "react-dom/client";
+import { App } from "./app.js";
+import "./styles.css";
+
+const rootElement = document.getElementById("root");
+
+if (!rootElement) {
+  throw new Error("Root element not found");
+}
+
+createRoot(rootElement).render(
+  <StrictMode>
+    <App />
+  </StrictMode>,
+);