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>

gateway/internal/grpcapi/observability.go

@@ -8,7 +8,7 @@ import (
 
 	"galaxy/gateway/internal/logging"
 	"galaxy/gateway/internal/telemetry"
-	gatewayv1 "galaxy/gateway/proto/galaxy/gateway/v1"
+	edgev1 "galaxy/gateway/proto/edge/v1"
 
 	"go.opentelemetry.io/otel/attribute"
 	"go.uber.org/zap"
@@ -78,9 +78,9 @@ func recordEdgeRequest(logger *zap.Logger, metrics *telemetry.Runtime, ctx conte
 
 func envelopeFieldsFromRequest(req any) (messageType string, requestID string, traceID string) {
 	switch typed := req.(type) {
-	case *gatewayv1.ExecuteCommandRequest:
+	case *edgev1.ExecuteCommandRequest:
 		return typed.GetMessageType(), typed.GetRequestId(), typed.GetTraceId()
-	case *gatewayv1.SubscribeEventsRequest:
+	case *edgev1.SubscribeEventsRequest:
 		return typed.GetMessageType(), typed.GetRequestId(), typed.GetTraceId()
 	default:
 		return "", "", ""
@@ -88,7 +88,7 @@ func envelopeFieldsFromRequest(req any) (messageType string, requestID string, t
 }
 
 func resultCodeFromResponse(resp any) string {
-	typed, ok := resp.(*gatewayv1.ExecuteCommandResponse)
+	typed, ok := resp.(*edgev1.ExecuteCommandResponse)
 	if !ok {
 		return ""
 	}