feat(vk): embed the game as a VK Mini App

Mirror the Telegram Mini App wrapper for VK: the SPA loads at a new /vk/
entry, authenticates from VK's signed launch parameters, and provisions a
'vk' platform identity — the minimum to run the game in VK test mode.

- Gateway verifies the launch signature in-process (internal/vkauth:
  HMAC-SHA256 over the sorted vk_* params under GATEWAY_VK_APP_SECRET,
  base64url) — a pure offline check, no side-service. New auth.vk op
  (gated on the secret), backendclient.VKAuth, /vk/ SPA mount.
- Backend: KindVK + ProvisionVK/vkSeed, /sessions/vk handler, identity
  kind widened to include 'vk' (migration 00005, expand-contract).
- UI: src/lib/vk.ts (VK Bridge, lazy-imported), bootVK + the /vk/ boot
  dispatch, encodeVKLogin + authVK across transport/client/mock. VK omits
  the name from the signed params, so the client reads it via
  VKWebAppGetUserInfo as an unsigned display seed.
- Deploy: /vk in the edge Caddyfile, GATEWAY_VK_APP_SECRET wired through
  compose + .env.example + CI (TEST_) + prod-deploy (PROD_).
- Admin console: surface the VK user id (link to the VK profile) next to
  the Telegram id on the user card.
- Docs: ARCHITECTURE §12/§13, FUNCTIONAL (+ _ru), gateway README; VK
  integration reference under .claude/.

Signature algorithm verified against dev.vk.com plus independent Node/Python
references and a %2C edge-case vector.

gateway/internal/transcode/transcode.go

@@ -13,12 +13,14 @@ import (
 
 	"scrabble/gateway/internal/backendclient"
 	"scrabble/gateway/internal/connector"
+	"scrabble/gateway/internal/vkauth"
 	fb "scrabble/pkg/fbs/scrabblefb"
 )
 
 // Message types in the vertical slice.
 const (
 	MsgAuthTelegram   = "auth.telegram"
+	MsgAuthVK         = "auth.vk"
 	MsgAuthGuest      = "auth.guest"
 	MsgAuthEmailReq   = "auth.email.request"
 	MsgAuthEmailLogin = "auth.email.login"
@@ -89,8 +91,9 @@ type TelegramValidator interface {
 
 // NewRegistry builds the slice's message-type catalog over the backend client.
 // The Telegram auth op is registered only when a validator is supplied (the
-// connector is configured); otherwise auth.telegram is simply unknown.
-func NewRegistry(backend *backendclient.Client, tg TelegramValidator) *Registry {
+// connector is configured); otherwise auth.telegram is simply unknown. Optional ops
+// (e.g. WithVKAuth) are applied last from opts.
+func NewRegistry(backend *backendclient.Client, tg TelegramValidator, opts ...Option) *Registry {
 	r := &Registry{ops: make(map[string]Op)}
 	if tg != nil {
 		r.ops[MsgAuthTelegram] = Op{Handler: authTelegramHandler(backend, tg)}
@@ -126,9 +129,27 @@ func NewRegistry(backend *backendclient.Client, tg TelegramValidator) *Registry
 	r.ops[MsgFeedbackUnread] = Op{Handler: feedbackUnreadHandler(backend), Auth: true}
 	registerSocialOps(r, backend)
 	registerLinkOps(r, backend, tg)
+	for _, opt := range opts {
+		opt(r, backend)
+	}
 	return r
 }
 
+// Option configures an optional registry operation at construction. It is kept out of
+// NewRegistry's positional signature so existing call sites stay unaffected.
+type Option func(r *Registry, backend *backendclient.Client)
+
+// WithVKAuth registers the VK Mini App auth op (auth.vk), which verifies launch params
+// in-process under the VK app secret. A blank secret leaves auth.vk unregistered, so
+// the op is simply unknown wherever VK is not configured.
+func WithVKAuth(secret string) Option {
+	return func(r *Registry, backend *backendclient.Client) {
+		if secret != "" {
+			r.ops[MsgAuthVK] = Op{Handler: authVKHandler(backend, secret)}
+		}
+	}
+}
+
 // Lookup returns the operation for messageType, and whether it is registered.
 func (r *Registry) Lookup(messageType string) (Op, bool) {
 	op, ok := r.ops[messageType]
@@ -146,6 +167,9 @@ func DomainCode(err error) (string, bool) {
 	if errors.Is(err, connector.ErrInvalidInitData) {
 		return "invalid_init_data", true
 	}
+	if errors.Is(err, vkauth.ErrInvalid) {
+		return "invalid_vk_params", true
+	}
 	if errors.Is(err, connector.ErrInvalidLoginWidget) {
 		return "invalid_login_widget", true
 	}
@@ -175,6 +199,25 @@ func authTelegramHandler(backend *backendclient.Client, tg TelegramValidator) Ha
 	}
 }
 
+// authVKHandler verifies a VK Mini App launch in-process (HMAC over the signed vk_*
+// params under the app secret) and provisions/finds the bound account. Unlike Telegram,
+// VK omits the user's name from the signed params, so the client-supplied display_name
+// rides the wire as a cosmetic seed for a brand-new account.
+func authVKHandler(backend *backendclient.Client, secret string) Handler {
+	return func(ctx context.Context, req Request) ([]byte, error) {
+		in := fb.GetRootAsVKLoginRequest(req.Payload, 0)
+		user, err := vkauth.Verify(string(in.Params()), secret)
+		if err != nil {
+			return nil, err
+		}
+		sess, err := backend.VKAuth(ctx, user.ExternalID, user.Language, string(in.DisplayName()), string(in.BrowserTz()))
+		if err != nil {
+			return nil, err
+		}
+		return encodeSession(sess), nil
+	}
+}
+
 func authGuestHandler(backend *backendclient.Client) Handler {
 	return func(ctx context.Context, req Request) ([]byte, error) {
 		// The guest bootstrap historically carried no payload; the detected zone is