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/prod.env

@@ -0,0 +1,12 @@
+DISCORD_CLIENT_ID="op://Environment Variables - Naomi/Elysium/discord client id"
+DISCORD_CLIENT_SECRET="op://Environment Variables - Naomi/Elysium/discord client secret"
+DISCORD_REDIRECT_URI="op://Environment Variables - Naomi/Elysium/discord redirect uri"
+JWT_SECRET="op://Environment Variables - Naomi/Elysium/jwt secret"
+DATABASE_URL="op://Environment Variables - Naomi/Elysium/mongo url"
+ANTI_CHEAT_SECRET="op://Environment Variables - Naomi/Elysium/anti cheat secret"
+PORT="op://Environment Variables - Naomi/Elysium/port"
+CORS_ORIGIN="op://Environment Variables - Naomi/Elysium/origin"
+DISCORD_MILESTONE_WEBHOOK="op://Environment Variables - Naomi/Elysium/discord milestone webhook"
+DISCORD_BOT_TOKEN="op://Environment Variables - Naomi/Elysium/discord bot token"
+DISCORD_GUILD_ID="op://Environment Variables - Naomi/Elysium/discord guild id"
+DISCORD_APOTHEOSIS_ROLE_ID="op://Environment Variables - Naomi/Elysium/discord apotheosis role id"