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>

site/.vitepress/config.ts

@@ -0,0 +1,55 @@
+import { defineConfig } from "vitepress";
+
+// Galaxy project site. The single-origin deployment serves this static
+// build at the root (`/`); the game UI lives under `/game/`. The site is
+// Markdown-first with the default theme's two-column navigation (left:
+// chapters; right: on-this-page), LaTeX math, and a minimal monospace
+// theme. Internationalisation uses VitePress `locales`, which renders the
+// built-in language switcher in the nav bar.
+export default defineConfig({
+  title: "Galaxy",
+  description: "Galaxy — a turn-based space strategy game.",
+  cleanUrls: true,
+  // READMEs (this dir's and any future per-section ones) are developer
+  // docs, not site pages.
+  srcExclude: ["**/README.md"],
+  // The game UI is served from `/game/` by the edge Caddy, not by
+  // VitePress, so its links must skip the dead-link checker.
+  ignoreDeadLinks: [/^\/game\//],
+  markdown: {
+    // LaTeX via markdown-it-mathjax3: inline `$…$`, block `$$…$$`.
+    math: true,
+  },
+  themeConfig: {
+    outline: { level: [2, 3], label: "On this page" },
+  },
+  locales: {
+    root: {
+      label: "English",
+      lang: "en",
+      themeConfig: {
+        nav: [{ text: "Play", link: "/game/" }],
+        sidebar: [
+          {
+            text: "Galaxy",
+            items: [{ text: "Overview", link: "/" }],
+          },
+        ],
+      },
+    },
+    ru: {
+      label: "Русский",
+      lang: "ru",
+      link: "/ru/",
+      themeConfig: {
+        nav: [{ text: "Играть", link: "/game/" }],
+        sidebar: [
+          {
+            text: "Galaxy",
+            items: [{ text: "Обзор", link: "/ru/" }],
+          },
+        ],
+      },
+    },
+  },
+});

site/.vitepress/theme/custom.css

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+/*
+ * Minimal, restrained theme. No flashy hero or bright accents — the
+ * project site leans "nerdy" with a fixed-width type stack. System
+ * fonts first so nothing is downloaded.
+ */
+:root {
+	--vp-font-family-base: ui-monospace, "JetBrains Mono", "SF Mono",
+		"Fira Code", "DejaVu Sans Mono", Menlo, Consolas, monospace;
+	--vp-font-family-mono: var(--vp-font-family-base);
+}

site/.vitepress/theme/index.ts

@@ -0,0 +1,6 @@
+// Minimal theme: the default VitePress theme without its bundled Inter
+// font, plus a monospace type stack for the project's "nerdy" look.
+import DefaultTheme from "vitepress/theme-without-fonts";
+import "./custom.css";
+
+export default DefaultTheme;