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>

packages/types/package.json

@@ -0,0 +1,21 @@
+{
+  "name": "@elysium/types",
+  "version": "0.0.0",
+  "private": true,
+  "type": "module",
+  "main": "./prod/src/index.js",
+  "types": "./prod/src/index.d.ts",
+  "scripts": {
+    "build": "tsc -p tsconfig.json",
+    "lint": "eslint --max-warnings 0 src",
+    "test": "vitest run --coverage"
+  },
+  "devDependencies": {
+    "@nhcarrigan/eslint-config": "5.2.0",
+    "@nhcarrigan/typescript-config": "4.0.0",
+    "@vitest/coverage-v8": "3.0.8",
+    "eslint": "9.22.0",
+    "typescript": "5.8.2",
+    "vitest": "3.0.8"
+  }
+}