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/freshness_replay.go

@@ -7,7 +7,7 @@ import (
 
 	"galaxy/gateway/internal/clock"
 	"galaxy/gateway/internal/replay"
-	gatewayv1 "galaxy/gateway/proto/galaxy/gateway/v1"
+	edgev1 "galaxy/gateway/proto/edge/v1"
 
 	"google.golang.org/grpc"
 	"google.golang.org/grpc/codes"
@@ -19,9 +19,9 @@ const minimumReplayReservationTTL = time.Millisecond
 // freshnessAndReplayService applies freshness and anti-replay checks after
 // client-signature verification and before later policy or routing steps run.
 type freshnessAndReplayService struct {
-	gatewayv1.UnimplementedEdgeGatewayServer
+	edgev1.UnimplementedGatewayServer
 
-	delegate        gatewayv1.EdgeGatewayServer
+	delegate        edgev1.GatewayServer
 	clock           clock.Clock
 	replayStore     replay.Store
 	freshnessWindow time.Duration
@@ -29,7 +29,7 @@ type freshnessAndReplayService struct {
 
 // ExecuteCommand verifies request freshness and replay protection before
 // delegating to the configured service implementation.
-func (s freshnessAndReplayService) ExecuteCommand(ctx context.Context, req *gatewayv1.ExecuteCommandRequest) (*gatewayv1.ExecuteCommandResponse, error) {
+func (s freshnessAndReplayService) ExecuteCommand(ctx context.Context, req *edgev1.ExecuteCommandRequest) (*edgev1.ExecuteCommandResponse, error) {
 	if err := s.verifyFreshnessAndReplay(ctx); err != nil {
 		return nil, err
 	}
@@ -39,7 +39,7 @@ func (s freshnessAndReplayService) ExecuteCommand(ctx context.Context, req *gate
 
 // SubscribeEvents verifies request freshness and replay protection before
 // delegating to the configured service implementation.
-func (s freshnessAndReplayService) SubscribeEvents(req *gatewayv1.SubscribeEventsRequest, stream grpc.ServerStreamingServer[gatewayv1.GatewayEvent]) error {
+func (s freshnessAndReplayService) SubscribeEvents(req *edgev1.SubscribeEventsRequest, stream grpc.ServerStreamingServer[edgev1.GatewayEvent]) error {
 	if err := s.verifyFreshnessAndReplay(stream.Context()); err != nil {
 		return err
 	}
@@ -49,7 +49,7 @@ func (s freshnessAndReplayService) SubscribeEvents(req *gatewayv1.SubscribeEvent
 
 // newFreshnessAndReplayService wraps delegate with the freshness and replay
 // gate.
-func newFreshnessAndReplayService(delegate gatewayv1.EdgeGatewayServer, clk clock.Clock, replayStore replay.Store, freshnessWindow time.Duration) gatewayv1.EdgeGatewayServer {
+func newFreshnessAndReplayService(delegate edgev1.GatewayServer, clk clock.Clock, replayStore replay.Store, freshnessWindow time.Duration) edgev1.GatewayServer {
 	return freshnessAndReplayService{
 		delegate:        delegate,
 		clock:           clk,
@@ -92,4 +92,4 @@ func (unavailableReplayStore) Reserve(context.Context, string, string, time.Dura
 	return errors.New("replay store is unavailable")
 }
 
-var _ gatewayv1.EdgeGatewayServer = freshnessAndReplayService{}
+var _ edgev1.GatewayServer = freshnessAndReplayService{}