feat(ads): VK post-move interstitial + retire deprecated hint_balance/paid_account

Interstitial video after a confirmed play or a hint, VK-only, offline
banner-only. The gate is client-mirrored: the backend puts the config
cooldowns (global 5m / vs_ai 30m / hint 1m) and a suppressed flag (the
no-ads / no_banner gate, same as the banner) on Profile.ads via adsFor;
the client self-gates on a per-kind last-shown time in localStorage, with
the VITE_ADS_STUB contour "ad fired" toast. Never fires after a pass,
exchange or resign. maybeShowInterstitial + vkShowInterstitial; the codec
and gateway transcode carry the ads block.

Also retires the deprecated accounts.hint_balance / paid_account domain
usage (expand-contract, code only — the columns stay for a later DROP so
image rollback stays DB-safe): drop the Account fields and their scan, the
dead account.SpendHint, account.GrantHints and the admin grant-hints
action; the in-game hint display now comes wholly from the payments hint
benefit. Banner eligibility and account merge no longer read the legacy
flags.

Tests: ads.test.ts (the client-mirrored gate), the codec ads round-trip,
the gateway ads transcode test, and a profile ads-config integration test
(cooldowns + suppressed under no-ads / no_banner). Docs: PAYMENTS §10 (+ru)
interstitial, the decision amends, backend README, the plan.

backend/internal/server/banner.go

@@ -57,9 +57,9 @@ type bannerTimingsDTO struct {
 func (s *Server) profileResponse(ctx context.Context, acc account.Account) profileResponse {
 	r := profileResponseFor(acc)
 	// Resolve the payments gate once (execution context + present sources) and feed it to both
-	// the hint count and the banner. The profile hint balance now comes from the payments benefit
-	// (context-aware), not the deprecated accounts.hint_balance column; on any failure the legacy
-	// value from profileResponseFor (zeroed in production) stands.
+	// the hint count and the banner. The profile hint balance comes from the payments benefit
+	// (context-aware); the deprecated accounts.hint_balance column is no longer read, so on any
+	// failure the fallback from profileResponseFor is a plain 0.
 	cxt, present, err := s.walletGate(ctx, acc.ID)
 	if err != nil {
 		s.log.Warn("profile: wallet gate failed", zap.String("account", acc.ID.String()), zap.Error(err))
@@ -71,6 +71,7 @@ func (s *Server) profileResponse(ctx context.Context, acc account.Account) profi
 		}
 	}
 	r.Banner = s.bannerFor(ctx, acc, cxt, present)
+	r.Ads = s.adsFor(ctx, acc, cxt, present)
 	s.fillLinkedIdentities(ctx, &r, acc.ID)
 	r.DictVersions = s.currentDictVersions()
 	return r
@@ -177,6 +178,44 @@ func (s *Server) bannerFor(ctx context.Context, acc account.Account, cxt payment
 	}
 }
 
+// adsDTO is the post-move interstitial config in the profile: the client-mirrored cooldowns
+// (seconds) and whether ads are suppressed in the context (a no-ads benefit applicable here, or the
+// no_banner role). The client shows a VK interstitial after a confirmed move / hint only when not
+// suppressed and the mirrored cooldown has elapsed.
+type adsDTO struct {
+	CooldownGlobalS int  `json:"cooldown_global_s"`
+	CooldownVsAiS   int  `json:"cooldown_vs_ai_s"`
+	CooldownHintS   int  `json:"cooldown_hint_s"`
+	Suppressed      bool `json:"suppressed"`
+}
+
+// adsFor builds the profile interstitial-ad config: the cooldowns and whether ads are suppressed
+// here (the same no-ads / no_banner gate as the banner). A read failure logs and yields a suppressed
+// block (fail-safe: no interstitial), so the profile still succeeds.
+func (s *Server) adsFor(ctx context.Context, acc account.Account, cxt payments.Context, present []payments.Source) *adsDTO {
+	if s.payments == nil {
+		return nil
+	}
+	global, vsAi, hint, err := s.payments.InterstitialCooldowns(ctx)
+	if err != nil {
+		s.log.Warn("profile: ad cooldowns read failed", zap.String("account", acc.ID.String()), zap.Error(err))
+		return &adsDTO{Suppressed: true}
+	}
+	suppressed := false
+	if adFree, aerr := s.payments.AdFree(ctx, acc.ID, cxt, present); aerr != nil {
+		s.log.Warn("profile: ad-free read failed", zap.String("account", acc.ID.String()), zap.Error(aerr))
+		suppressed = true // fail-safe: suppress the interstitial when eligibility is unknown
+	} else {
+		suppressed = adFree
+	}
+	if !suppressed {
+		if noBanner, berr := s.accounts.HasRole(ctx, acc.ID, account.RoleNoBanner); berr == nil {
+			suppressed = noBanner
+		}
+	}
+	return &adsDTO{CooldownGlobalS: global, CooldownVsAiS: vsAi, CooldownHintS: hint, Suppressed: suppressed}
+}
+
 // bannerCampaignFromActive flattens a resolved campaign into its wire DTO,
 // projecting each optional colour set into its three "#rrggbb" fields (empty when
 // the set is absent, so JSON omitempty drops them).