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/site-build.yaml

@@ -0,0 +1,47 @@
+name: Build · Site
+
+# Builds the VitePress project site so a broken site change fails its PR.
+# The dev-deploy / prod-build workflows build and ship the site
+# separately; this is the fast PR gate. No `!**/*.md` exclusion — the
+# site is Markdown, so content changes must be exercised too.
+
+on:
+  push:
+    paths:
+      - 'site/**'
+      - '.gitea/workflows/site-build.yaml'
+  pull_request:
+    paths:
+      - 'site/**'
+      - '.gitea/workflows/site-build.yaml'
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    defaults:
+      run:
+        shell: bash
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up pnpm
+        uses: pnpm/action-setup@v4
+        with:
+          version: 11.0.7
+          dest: ${{ runner.temp }}/setup-pnpm
+
+      - name: Set up Node
+        uses: actions/setup-node@v4
+        with:
+          node-version: 22
+          cache: pnpm
+          cache-dependency-path: site/pnpm-lock.yaml
+
+      - name: Install site dependencies
+        working-directory: site
+        run: pnpm install --frozen-lockfile
+
+      - name: Build project site
+        working-directory: site
+        run: pnpm build