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>

ui/frontend/src/lib/active-view/battle.svelte

@@ -12,6 +12,7 @@ header now — we just hand the routes down as callbacks so the
 viewer keeps its prop-driven contract.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { getContext } from "svelte";
 	import { goto } from "$app/navigation";
 
@@ -126,10 +127,10 @@ viewer keeps its prop-driven contract.
 	});
 
 	function backToReport() {
-		goto(`/games/${gameId}/report`);
+		goto(withBase(`/games/${gameId}/report`));
 	}
 	function backToMap() {
-		goto(`/games/${gameId}/map`);
+		goto(withBase(`/games/${gameId}/map`));
 	}
 </script>
 

ui/frontend/src/lib/active-view/designer-science.svelte

@@ -25,6 +25,7 @@ fractions is a Phase 21 decision documented in
 `ui/docs/science-designer-ux.md`.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { getContext, tick } from "svelte";
 	import { goto } from "$app/navigation";
 	import { page } from "$app/state";
@@ -125,7 +126,7 @@ fractions is a Phase 21 decision documented in
 	}
 
 	function backToTable(): void {
-		void goto(`/games/${gameId}/table/sciences`);
+		void goto(withBase(`/games/${gameId}/table/sciences`));
 	}
 
 	async function save(): Promise<void> {

ui/frontend/src/lib/active-view/map.svelte

@@ -20,6 +20,7 @@ Phase 29 wires the wrap-mode toggle on top of the per-game `wrapMode`
 preference the store already manages.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { getContext, onDestroy, onMount, untrack } from "svelte";
 	import { goto } from "$app/navigation";
 	import { page } from "$app/state";
@@ -636,14 +637,14 @@ preference the store already manages.
 				const gameId = page.params.id ?? "";
 				const turn = store?.report?.turn ?? 0;
 				void goto(
-					`/games/${gameId}/battle/${target.battleId}?turn=${turn}`,
+					withBase(`/games/${gameId}/battle/${target.battleId}?turn=${turn}`),
 				);
 				break;
 			}
 			case "bombing": {
 				const gameId = page.params.id ?? "";
 				void goto(
-					`/games/${gameId}/report#report-bombings`,
+					withBase(`/games/${gameId}/report#report-bombings`),
 				).then(() => {
 					if (typeof document === "undefined") return;
 					const row = document.querySelector(

ui/frontend/src/lib/active-view/report/report-toc.svelte

@@ -20,6 +20,7 @@ The active section is computed by the orchestrator
 `activeSlug` prop. The TOC itself owns no observers.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { goto } from "$app/navigation";
 
 	import { i18n, type TranslationKey } from "$lib/i18n/index.svelte";
@@ -62,7 +63,7 @@ The active section is computed by the orchestrator
 	}
 
 	async function backToMap(): Promise<void> {
-		await goto(`/games/${gameId}/map`);
+		await goto(withBase(`/games/${gameId}/map`));
 	}
 </script>
 

ui/frontend/src/lib/active-view/report/section-battles.svelte

@@ -7,6 +7,7 @@ monospace `<span>`; the rewire here is the one-liner the Phase 23
 decision log called out.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { getContext } from "svelte";
 	import { page } from "$app/state";
 
@@ -47,7 +48,7 @@ decision log called out.
 					</span>
 					<a
 						class="uuid"
-						href={`/games/${gameId}/battle/${b.id}?turn=${turn}`}
+						href={withBase(`/games/${gameId}/battle/${b.id}?turn=${turn}`)}
 						data-testid="report-battle-row"
 						data-id={b.id}
 					>{b.id}</a>

ui/frontend/src/lib/active-view/table-sciences.svelte

@@ -17,6 +17,7 @@ The component sits inside the active-view slot owned by
 data fetching is performed here — the layout is responsible.
 -->
 <script lang="ts">
+	import { withBase } from "$lib/paths";
 	import { getContext } from "svelte";
 	import { goto } from "$app/navigation";
 	import { page } from "$app/state";
@@ -117,11 +118,11 @@ data fetching is performed here — the layout is responsible.
 	}
 
 	function openDesigner(name: string): void {
-		void goto(`/games/${gameId}/designer/science/${encodeURIComponent(name)}`);
+		void goto(withBase(`/games/${gameId}/designer/science/${encodeURIComponent(name)}`));
 	}
 
 	function newScience(): void {
-		void goto(`/games/${gameId}/designer/science`);
+		void goto(withBase(`/games/${gameId}/designer/science`));
 	}
 
 	async function deleteScience(name: string): Promise<void> {