docs: document elysium project and update nav badge

src/components/navigation.ts

@@ -573,7 +573,7 @@ export const navigation = [
       {
         label: "Elysium",
         link: "/projects/elysium",
-        badge: { text: "unreleased", variant: "danger" },
+        badge: { text: "v0.5.0", variant: "caution" },
       },
       {
         label: "Elaria",

src/content/docs/projects/elysium.md

@@ -6,33 +6,66 @@ Elysium (hereinafter the "Application") is an idle RPG in the browser.
 
 ## 1. User Documentation
 
-:::note
-This section is coming soon!
-:::
+The Application provides an incremental/idler gameplay loop with progression systems including:
 
-This section is for those interacting with a live instance of the Application.
+1. Adventurer hiring and resource scaling.
+2. Zone exploration and boss encounters.
+3. Questing and crafting systems.
+4. Prestige, transcendence, and apotheosis reset layers.
+5. Character profile, titles, and leaderboard visibility.
+
+The API source includes routes for game state, combat, exploration, crafting, progression resets, leaderboards, and profiles (`apps/api/src/index.ts`).
+
+This project is currently marked as work in progress in the public project feed.
 
 ## 2. Technical Documentation
 
-:::note
-This section is coming soon!
-:::
+Elysium is a pnpm monorepo with two primary applications and a shared package.
 
-This section is for those interested in running their own instance of the Application.
+Workspace layout:
+
+1. `apps/web`: React + Vite frontend (`@elysium/web`).
+2. `apps/api`: Hono-based API service (`@elysium/api`).
+3. `packages/types`: shared type definitions (`@elysium/types`).
+
+Current versions in repository manifests:
+
+1. Root package: `0.5.0`.
+2. API package: `0.5.0`.
+3. Web package: `0.5.0`.
+
+Root commands:
+
+1. `pnpm install`
+2. `pnpm dev`
+3. `pnpm build`
+4. `pnpm test`
+
+API runtime notes:
+
+1. Uses `op run --env-file=./prod.env` for secret injection.
+2. Exposes a health endpoint at `GET /health`.
+3. Uses Prisma client/database tooling and Hono route modules.
 
 ## 3. Legal Documentation
 
-:::note
-This section is coming soon!
-:::
+The Application inherits nhcarrigan's global legal documents:
 
-This section is for expansions to our legal policies specific to the Application.
+1. Privacy Policy: https://docs.nhcarrigan.com/#/privacy
+2. Terms of Service: https://docs.nhcarrigan.com/#/terms
+3. License: https://docs.nhcarrigan.com/#/license
+
+Repository references:
+
+1. `PRIVACY.md`
+2. `TERMS.md`
+3. `LICENSE.md`
 
 ## 4. Contributing Documentation
 
-:::note
-This section is coming soon!
-:::
+Contribution guidance points to the shared docs portal:
 
-This section is for documentation related to contributing to the Application's codebase.
+1. https://docs.nhcarrigan.com/#/contributing
+
+The repository also includes a manual verification checklist in `verify.md` for gameplay flows that are not fully covered by automated tests.