feat(account): seed the time zone from the client's detected offset at creation

A new account's time_zone defaulted to 'UTC' until the player saved a profile, so the
robot's sleep window and the turn-timeout away-window sweeper — both anchored to the
account zone via account.ResolveZone — ran on UTC for every fresh player, skewing
robot-game timing until a manual Settings save. Seed the zone at creation instead, from
the client's detected "±HH:MM" offset.

- Carry browser_tz on the three account-creating auth requests (TelegramLoginRequest,
  GuestLoginRequest, EmailRequestRequest — the email account is provisioned at the
  code-request step, not at login) through the fbs envelope (+ Go/TS codegen), the
  gateway transcode + backend client, and the backend auth handlers into
  ProvisionTelegram / ProvisionGuest / ProvisionEmail.
- create() now writes time_zone explicitly: the validated detected offset, or 'UTC'
  (equal to the column default) when absent or malformed — deterministic, never guessed.
  The column is already NOT NULL DEFAULT 'UTC', so no migration is needed and existing
  accounts keep 'UTC'. An existing account is never overwritten on re-login.
- A detected zero offset is stored as "+00:00" (the zone is known and equals UTC),
  distinct from the "UTC" default that means "unknown" — which the feedback console's
  three-zone Filed display already reflects.
- Guard the guest handler against an empty payload (the bootstrap historically carried
  none) so it degrades to no-seed rather than panicking in GetRootAs*.
- Tests: zone seeding across Telegram/guest/email plus the "+00:00"/malformed/empty
  cases and the not-overwrite rule; codec round-trip for the three auth encoders.
  ARCHITECTURE + FUNCTIONAL(+ru) updated.

gateway/internal/backendclient/api.go

@@ -184,8 +184,10 @@ type ChatResp struct {
 }
 
 // TelegramAuth provisions/finds the Telegram account and mints a session, seeding a
-// brand-new account's display name and language from the validated launch fields.
-func (c *Client) TelegramAuth(ctx context.Context, externalID, languageCode, username, firstName string) (SessionResp, error) {
+// brand-new account's display name and language from the validated launch fields and
+// its time zone from browserTz (the client's detected "±HH:MM" UTC offset; first
+// contact only).
+func (c *Client) TelegramAuth(ctx context.Context, externalID, languageCode, username, firstName, browserTz string) (SessionResp, error) {
 	var out SessionResp
 	err := c.do(ctx, http.MethodPost, "/api/v1/internal/sessions/telegram", "", "",
 		map[string]string{
@@ -193,6 +195,7 @@ func (c *Client) TelegramAuth(ctx context.Context, externalID, languageCode, use
 			"language_code": languageCode,
 			"username":      username,
 			"first_name":    firstName,
+			"browser_tz":    browserTz,
 		}, &out)
 	return out, err
 }
@@ -243,17 +246,21 @@ func (c *Client) ChatAccessByUser(ctx context.Context, userID string) (ChatAcces
 	return out, err
 }
 
-// GuestAuth provisions a guest account and mints a session.
-func (c *Client) GuestAuth(ctx context.Context) (SessionResp, error) {
+// GuestAuth provisions a guest account and mints a session, seeding its time zone
+// from browserTz (the client's detected "±HH:MM" UTC offset).
+func (c *Client) GuestAuth(ctx context.Context, browserTz string) (SessionResp, error) {
 	var out SessionResp
-	err := c.do(ctx, http.MethodPost, "/api/v1/internal/sessions/guest", "", "", struct{}{}, &out)
+	err := c.do(ctx, http.MethodPost, "/api/v1/internal/sessions/guest", "", "",
+		map[string]string{"browser_tz": browserTz}, &out)
 	return out, err
 }
 
-// EmailRequest asks the backend to mail a login code.
-func (c *Client) EmailRequest(ctx context.Context, email string) error {
+// EmailRequest asks the backend to mail a login code, provisioning the account on
+// first contact; browserTz (the client's detected "±HH:MM" UTC offset) seeds the new
+// account's time zone, since the email account is created here, not at login.
+func (c *Client) EmailRequest(ctx context.Context, email, browserTz string) error {
 	return c.do(ctx, http.MethodPost, "/api/v1/internal/sessions/email/request", "", "",
-		map[string]string{"email": email}, nil)
+		map[string]string{"email": email, "browser_tz": browserTz}, nil)
 }
 
 // EmailLogin verifies a login code and mints a session.