feat(deploy): single-origin path-based deployment + project site

Serve the whole stack behind one host: site at /, game UI at /game/,
gateway REST at /api + /healthz, Connect at /rpc (prefix stripped by the
edge Caddy). The built artifact is domain-agnostic — the UI talks to the
gateway same-origin via relative URLs, so the same bundle runs under any
host with no rebuild and with CORS disabled.

- Rename the Connect proto service galaxy.gateway.v1.EdgeGateway ->
  edge.v1.Gateway; regenerate Go + TS; public path /rpc/edge.v1.Gateway.
- Move the game UI under base path /game (env BASE_PATH); make the
  manifest, service-worker scope, WASM loader, and all navigation
  base-aware via a withBase helper.
- Relative API + /rpc Connect prefix; Vite dev proxy mirrors the strip.
- Rewrite the edge Caddy (dev + prod) for path-based routing; empty CORS
  allow-lists (same-origin); single host.
- New VitePress project site (site/): i18n en/ru with switcher, LaTeX
  math, minimal monospace theme; built and served at /.
- dev-deploy compose/Makefile + CI (dev-deploy, prod-build, new
  site-build) build and seed the site; probes hit /, /game/, /healthz.
- Sync docs (ARCHITECTURE, gateway README/openapi, dev-deploy &
  local-dev READMEs, CLAUDE.md, ui/PLAN).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

.gitea/workflows/prod-build.yaml

@@ -16,6 +16,7 @@ on:
       - 'game/**'
       - 'pkg/**'
       - 'ui/**'
+      - 'site/**'
       - 'go.work'
       - 'go.work.sum'
       - '.gitea/workflows/prod-build.yaml'
@@ -93,7 +94,11 @@ jobs:
       - name: Build UI bundle
         working-directory: ui/frontend
         env:
-          VITE_GATEWAY_BASE_URL: https://api.galaxy.com
+          # Single-origin deployment: an empty base URL means the
+          # gateway shares the document origin (REST at /api, Connect at
+          # /rpc). The game UI is served under the /game/ base path.
+          VITE_GATEWAY_BASE_URL: ""
+          BASE_PATH: /game
         run: |
           # Production response-signing public key is not in the repo
           # yet (the dev key in `tools/local-dev/keys/` is for dev
@@ -104,6 +109,14 @@ jobs:
           export VITE_GATEWAY_RESPONSE_PUBLIC_KEY="$(grep -E '^VITE_GATEWAY_RESPONSE_PUBLIC_KEY=' .env.development | cut -d= -f2)"
           pnpm build
 
+      - name: Install site dependencies
+        working-directory: site
+        run: pnpm install --frozen-lockfile
+
+      - name: Build project site
+        working-directory: site
+        run: pnpm build
+
       - name: Save images as artifact bundles
         run: |
           mkdir -p artifacts
@@ -115,6 +128,8 @@ jobs:
             | gzip >"artifacts/game-engine-${{ steps.tag.outputs.tag }}.tar.gz"
           tar -C ui/frontend -czf \
             "artifacts/ui-dist-${{ steps.tag.outputs.tag }}.tar.gz" build
+          tar -C site/.vitepress -czf \
+            "artifacts/site-dist-${{ steps.tag.outputs.tag }}.tar.gz" dist
 
       - name: Upload images
         uses: actions/upload-artifact@v4