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.

gateway/internal/backendclient/api.go

@@ -37,6 +37,8 @@ type ProfileResp struct {
 	// Banner is the advertising-banner block, present only for a viewer eligible to
 	// see the banner. The gateway forwards it verbatim into the Profile payload.
 	Banner *BannerResp `json:"banner,omitempty"`
+	// Ads is the post-move interstitial config (cooldowns + suppressed) for the client-mirrored gate.
+	Ads *AdsResp `json:"ads,omitempty"`
 	// Email is the confirmed email ("" when none); TelegramLinked/VkLinked report an
 	// attached platform identity — they drive the profile's link/unlink/change controls.
 	Email          string `json:"email"`
@@ -47,6 +49,15 @@ type ProfileResp struct {
 	DictVersions []DictVersion `json:"dict_versions,omitempty"`
 }
 
+// AdsResp is the post-move interstitial config in the profile: the client-mirrored cooldowns
+// (seconds) and whether ads are suppressed in the caller's context.
+type AdsResp struct {
+	CooldownGlobalS int  `json:"cooldown_global_s"`
+	CooldownVsAiS   int  `json:"cooldown_vs_ai_s"`
+	CooldownHintS   int  `json:"cooldown_hint_s"`
+	Suppressed      bool `json:"suppressed"`
+}
+
 // DictVersion pairs a game variant's stable label with its current dictionary version.
 type DictVersion struct {
 	Variant string `json:"variant"`