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/galaxy-client.test.ts

@@ -16,10 +16,10 @@ import { createClient, createRouterTransport } from "@connectrpc/connect";
 import { describe, expect, test, vi } from "vitest";
 import { GalaxyClient } from "../src/api/galaxy-client";
 import {
-	EdgeGateway,
+	Gateway,
 	ExecuteCommandResponseSchema,
 	type ExecuteCommandRequest,
-} from "../src/proto/galaxy/gateway/v1/edge_gateway_pb";
+} from "../src/proto/edge/v1/edge_gateway_pb";
 import type {
 	Core,
 	RequestSigningFields,
@@ -48,7 +48,7 @@ describe("GalaxyClient.executeCommand", () => {
 		const sha256 = vi.fn(async () => new Uint8Array(32).fill(0x33));
 		let captured: ExecuteCommandRequest | undefined;
 		const transport = createRouterTransport(({ service }) => {
-			service(EdgeGateway, {
+			service(Gateway, {
 				executeCommand(req) {
 					captured = req;
 					return create(ExecuteCommandResponseSchema, {
@@ -66,7 +66,7 @@ describe("GalaxyClient.executeCommand", () => {
 				},
 			});
 		});
-		const edge = createClient(EdgeGateway, transport);
+		const edge = createClient(Gateway, transport);
 
 		const client = new GalaxyClient({
 			core,
@@ -115,7 +115,7 @@ describe("GalaxyClient.executeCommand", () => {
 			verifyPayloadHashImpl: () => true,
 		});
 		const transport = createRouterTransport(({ service }) => {
-			service(EdgeGateway, {
+			service(Gateway, {
 				executeCommand: () =>
 					create(ExecuteCommandResponseSchema, {
 						protocolVersion: "v1",
@@ -133,7 +133,7 @@ describe("GalaxyClient.executeCommand", () => {
 		});
 		const client = new GalaxyClient({
 			core,
-			edge: createClient(EdgeGateway, transport),
+			edge: createClient(Gateway, transport),
 			signer: async () => new Uint8Array(64),
 			sha256: async () => new Uint8Array(32),
 			deviceSessionId: "device-session-1",
@@ -153,7 +153,7 @@ describe("GalaxyClient.executeCommand", () => {
 			verifyPayloadHashImpl: () => false,
 		});
 		const transport = createRouterTransport(({ service }) => {
-			service(EdgeGateway, {
+			service(Gateway, {
 				executeCommand: () =>
 					create(ExecuteCommandResponseSchema, {
 						protocolVersion: "v1",
@@ -171,7 +171,7 @@ describe("GalaxyClient.executeCommand", () => {
 		});
 		const client = new GalaxyClient({
 			core,
-			edge: createClient(EdgeGateway, transport),
+			edge: createClient(Gateway, transport),
 			signer: async () => new Uint8Array(64),
 			sha256: async () => new Uint8Array(32),
 			deviceSessionId: "device-session-1",