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/tests/events.test.ts

@@ -16,10 +16,10 @@ import {
 	createRouterTransport,
 } from "@connectrpc/connect";
 import {
-	EdgeGateway,
+	Gateway,
 	GatewayEventSchema,
 	type GatewayEvent,
-} from "../src/proto/galaxy/gateway/v1/edge_gateway_pb";
+} from "../src/proto/edge/v1/edge_gateway_pb";
 
 let sessionStatus: "anonymous" | "authenticated" = "anonymous";
 const signOutSpy = vi.fn();
@@ -91,9 +91,9 @@ function buildEvent(eventType: string, payload: Uint8Array): GatewayEvent {
 
 function makeRouter(
 	streamFactory: () => AsyncIterable<GatewayEvent>,
-): ReturnType<typeof createClient<typeof EdgeGateway>> {
+): ReturnType<typeof createClient<typeof Gateway>> {
 	const transport = createRouterTransport(({ service }) => {
-		service(EdgeGateway, {
+		service(Gateway, {
 			executeCommand() {
 				throw new Error("not used in this test");
 			},
@@ -104,7 +104,7 @@ function makeRouter(
 			},
 		});
 	});
-	return createClient(EdgeGateway, transport);
+	return createClient(Gateway, transport);
 }
 
 describe("EventStream", () => {