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/api/vitest.config.ts

@@ -0,0 +1,23 @@
+import { defineConfig } from "vitest/config";
+
+export default defineConfig({
+  test: {
+    coverage: {
+      provider: "v8",
+      include: ["src/**/*.ts"],
+      exclude: [
+        "src/types/**/*.ts",
+        "src/db/client.ts",
+        "src/index.ts",
+        "src/data/materials.ts",
+      ],
+      thresholds: {
+        statements: 100,
+        branches: 100,
+        functions: 100,
+        lines: 100,
+      },
+    },
+    include: ["test/**/*.spec.ts"],
+  },
+});