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/proto/edge/v1/edge_gateway_pb.ts

@@ -1,22 +1,22 @@
 // @generated by protoc-gen-es v2.12.0 with parameter "target=ts"
-// @generated from file galaxy/gateway/v1/edge_gateway.proto (package galaxy.gateway.v1, syntax proto3)
+// @generated from file edge/v1/edge_gateway.proto (package edge.v1, syntax proto3)
 /* eslint-disable */
 
 import type { GenFile, GenMessage, GenService } from "@bufbuild/protobuf/codegenv2";
 import { fileDesc, messageDesc, serviceDesc } from "@bufbuild/protobuf/codegenv2";
-import { file_buf_validate_validate } from "../../../buf/validate/validate_pb";
+import { file_buf_validate_validate } from "../../buf/validate/validate_pb";
 import type { Message } from "@bufbuild/protobuf";
 
 /**
- * Describes the file galaxy/gateway/v1/edge_gateway.proto.
+ * Describes the file edge/v1/edge_gateway.proto.
  */
-export const file_galaxy_gateway_v1_edge_gateway: GenFile = /*@__PURE__*/
-  fileDesc("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", [file_buf_validate_validate]);
+export const file_edge_v1_edge_gateway: GenFile = /*@__PURE__*/
+  fileDesc("ChplZGdlL3YxL2VkZ2VfZ2F0ZXdheS5wcm90bxIHZWRnZS52MSKmAgoVRXhlY3V0ZUNvbW1hbmRSZXF1ZXN0EiEKEHByb3RvY29sX3ZlcnNpb24YASABKAlCB7pIBHICEAESIgoRZGV2aWNlX3Nlc3Npb25faWQYAiABKAlCB7pIBHICEAESHQoMbWVzc2FnZV90eXBlGAMgASgJQge6SARyAhABEh0KDHRpbWVzdGFtcF9tcxgEIAEoA0IHukgEIgIgABIbCgpyZXF1ZXN0X2lkGAUgASgJQge6SARyAhABEh4KDXBheWxvYWRfYnl0ZXMYBiABKAxCB7pIBHoCEAESHQoMcGF5bG9hZF9oYXNoGAcgASgMQge6SAR6AhABEhoKCXNpZ25hdHVyZRgIIAEoDEIHukgEegIQARIQCgh0cmFjZV9pZBgJIAEoCSKxAQoWRXhlY3V0ZUNvbW1hbmRSZXNwb25zZRIYChBwcm90b2NvbF92ZXJzaW9uGAEgASgJEhIKCnJlcXVlc3RfaWQYAiABKAkSFAoMdGltZXN0YW1wX21zGAMgASgDEhMKC3Jlc3VsdF9jb2RlGAQgASgJEhUKDXBheWxvYWRfYnl0ZXMYBSABKAwSFAoMcGF5bG9hZF9oYXNoGAYgASgMEhEKCXNpZ25hdHVyZRgHIAEoDCKeAgoWU3Vic2NyaWJlRXZlbnRzUmVxdWVzdBIhChBwcm90b2NvbF92ZXJzaW9uGAEgASgJQge6SARyAhABEiIKEWRldmljZV9zZXNzaW9uX2lkGAIgASgJQge6SARyAhABEh0KDG1lc3NhZ2VfdHlwZRgDIAEoCUIHukgEcgIQARIdCgx0aW1lc3RhbXBfbXMYBCABKANCB7pIBCICIAASGwoKcmVxdWVzdF9pZBgFIAEoCUIHukgEcgIQARIdCgxwYXlsb2FkX2hhc2gYBiABKAxCB7pIBHoCEAESGgoJc2lnbmF0dXJlGAcgASgMQge6SAR6AhABEhUKDXBheWxvYWRfYnl0ZXMYCCABKAwSEAoIdHJhY2VfaWQYCSABKAkisAEKDEdhdGV3YXlFdmVudBISCgpldmVudF90eXBlGAEgASgJEhAKCGV2ZW50X2lkGAIgASgJEhQKDHRpbWVzdGFtcF9tcxgDIAEoAxIVCg1wYXlsb2FkX2J5dGVzGAQgASgMEhQKDHBheWxvYWRfaGFzaBgFIAEoDBIRCglzaWduYXR1cmUYBiABKAwSEgoKcmVxdWVzdF9pZBgHIAEoCRIQCgh0cmFjZV9pZBgIIAEoCTKpAQoHR2F0ZXdheRJRCg5FeGVjdXRlQ29tbWFuZBIeLmVkZ2UudjEuRXhlY3V0ZUNvbW1hbmRSZXF1ZXN0Gh8uZWRnZS52MS5FeGVjdXRlQ29tbWFuZFJlc3BvbnNlEksKD1N1YnNjcmliZUV2ZW50cxIfLmVkZ2UudjEuU3Vic2NyaWJlRXZlbnRzUmVxdWVzdBoVLmVkZ2UudjEuR2F0ZXdheUV2ZW50MAFCJVojZ2FsYXh5L2dhdGV3YXkvcHJvdG8vZWRnZS92MTtlZGdldjFiBnByb3RvMw", [file_buf_validate_validate]);
 
 /**
- * @generated from message galaxy.gateway.v1.ExecuteCommandRequest
+ * @generated from message edge.v1.ExecuteCommandRequest
  */
-export type ExecuteCommandRequest = Message<"galaxy.gateway.v1.ExecuteCommandRequest"> & {
+export type ExecuteCommandRequest = Message<"edge.v1.ExecuteCommandRequest"> & {
   /**
    * protocol_version identifies the request envelope version. The gateway
    * accepts only the literal "v1" after required-field validation succeeds.
@@ -69,16 +69,16 @@ export type ExecuteCommandRequest = Message<"galaxy.gateway.v1.ExecuteCommandReq
 };
 
 /**
- * Describes the message galaxy.gateway.v1.ExecuteCommandRequest.
+ * Describes the message edge.v1.ExecuteCommandRequest.
  * Use `create(ExecuteCommandRequestSchema)` to create a new message.
  */
 export const ExecuteCommandRequestSchema: GenMessage<ExecuteCommandRequest> = /*@__PURE__*/
-  messageDesc(file_galaxy_gateway_v1_edge_gateway, 0);
+  messageDesc(file_edge_v1_edge_gateway, 0);
 
 /**
- * @generated from message galaxy.gateway.v1.ExecuteCommandResponse
+ * @generated from message edge.v1.ExecuteCommandResponse
  */
-export type ExecuteCommandResponse = Message<"galaxy.gateway.v1.ExecuteCommandResponse"> & {
+export type ExecuteCommandResponse = Message<"edge.v1.ExecuteCommandResponse"> & {
   /**
    * @generated from field: string protocol_version = 1;
    */
@@ -116,16 +116,16 @@ export type ExecuteCommandResponse = Message<"galaxy.gateway.v1.ExecuteCommandRe
 };
 
 /**
- * Describes the message galaxy.gateway.v1.ExecuteCommandResponse.
+ * Describes the message edge.v1.ExecuteCommandResponse.
  * Use `create(ExecuteCommandResponseSchema)` to create a new message.
  */
 export const ExecuteCommandResponseSchema: GenMessage<ExecuteCommandResponse> = /*@__PURE__*/
-  messageDesc(file_galaxy_gateway_v1_edge_gateway, 1);
+  messageDesc(file_edge_v1_edge_gateway, 1);
 
 /**
- * @generated from message galaxy.gateway.v1.SubscribeEventsRequest
+ * @generated from message edge.v1.SubscribeEventsRequest
  */
-export type SubscribeEventsRequest = Message<"galaxy.gateway.v1.SubscribeEventsRequest"> & {
+export type SubscribeEventsRequest = Message<"edge.v1.SubscribeEventsRequest"> & {
   /**
    * protocol_version identifies the request envelope version. The gateway
    * accepts only the literal "v1" after required-field validation succeeds.
@@ -179,16 +179,16 @@ export type SubscribeEventsRequest = Message<"galaxy.gateway.v1.SubscribeEventsR
 };
 
 /**
- * Describes the message galaxy.gateway.v1.SubscribeEventsRequest.
+ * Describes the message edge.v1.SubscribeEventsRequest.
  * Use `create(SubscribeEventsRequestSchema)` to create a new message.
  */
 export const SubscribeEventsRequestSchema: GenMessage<SubscribeEventsRequest> = /*@__PURE__*/
-  messageDesc(file_galaxy_gateway_v1_edge_gateway, 2);
+  messageDesc(file_edge_v1_edge_gateway, 2);
 
 /**
- * @generated from message galaxy.gateway.v1.GatewayEvent
+ * @generated from message edge.v1.GatewayEvent
  */
-export type GatewayEvent = Message<"galaxy.gateway.v1.GatewayEvent"> & {
+export type GatewayEvent = Message<"edge.v1.GatewayEvent"> & {
   /**
    * @generated from field: string event_type = 1;
    */
@@ -231,18 +231,18 @@ export type GatewayEvent = Message<"galaxy.gateway.v1.GatewayEvent"> & {
 };
 
 /**
- * Describes the message galaxy.gateway.v1.GatewayEvent.
+ * Describes the message edge.v1.GatewayEvent.
  * Use `create(GatewayEventSchema)` to create a new message.
  */
 export const GatewayEventSchema: GenMessage<GatewayEvent> = /*@__PURE__*/
-  messageDesc(file_galaxy_gateway_v1_edge_gateway, 3);
+  messageDesc(file_edge_v1_edge_gateway, 3);
 
 /**
- * @generated from service galaxy.gateway.v1.EdgeGateway
+ * @generated from service edge.v1.Gateway
  */
-export const EdgeGateway: GenService<{
+export const Gateway: GenService<{
   /**
-   * @generated from rpc galaxy.gateway.v1.EdgeGateway.ExecuteCommand
+   * @generated from rpc edge.v1.Gateway.ExecuteCommand
    */
   executeCommand: {
     methodKind: "unary";
@@ -250,7 +250,7 @@ export const EdgeGateway: GenService<{
     output: typeof ExecuteCommandResponseSchema;
   },
   /**
-   * @generated from rpc galaxy.gateway.v1.EdgeGateway.SubscribeEvents
+   * @generated from rpc edge.v1.Gateway.SubscribeEvents
    */
   subscribeEvents: {
     methodKind: "server_streaming";
@@ -258,5 +258,5 @@ export const EdgeGateway: GenService<{
     output: typeof GatewayEventSchema;
   },
 }> = /*@__PURE__*/
-  serviceDesc(file_galaxy_gateway_v1_edge_gateway, 0);
+  serviceDesc(file_edge_v1_edge_gateway, 0);