fix(ads): share one interstitial cooldown timer across kinds

Cooldowns were tracked per kind ({move,hint}), so a hint ad and a move ad
did not see each other: after a hinted move's ad the move timer was still
zero, and the next plain move fired an ad immediately — two ads within a
minute, under the cooldown. Track a single shared last-shown time; the kind
only selects the required gap (hint 1m, move 5m, vs_ai 30m) measured from the
last interstitial of any kind. A hint can still fire on its shorter gap
(D30's "independent" hint cooldown), but never stacks a second ad within a
cooldown.

Tests: a hint uses the shorter shared gap; a move does not stack onto a
just-shown hint ad.

docs/PAYMENTS.md

@@ -283,9 +283,10 @@ always shows real ads (a failed real ad must not credit).
 **Interstitial** (fullscreen after a confirmed play), **VK-only**, configurable server-side
 values. The gate is **client-mirrored**: the profile carries the cooldowns and a `suppressed`
 flag (the same no-ads / `no_banner` gate as the banner, resolved server-side in `adsFor`), and
-the client self-gates on the last-shown time **per kind** in `localStorage` — no per-move
-server round-trip. The contour `VITE_ADS_STUB` swaps the same "ad fired" toast for the real ad.
-Values:
+the client self-gates on a **single shared** last-shown time in `localStorage` — the kind only
+picks the required gap, so a hint ad and a move ad never fire within a cooldown of each other
+(one shared timer, not one per kind) — no per-move server round-trip. The contour
+`VITE_ADS_STUB` swaps the same "ad fired" toast for the real ad. Values:
 
 - Global cooldown **per user, across all games**, default **5 min**.
 - **`vs_ai` — 30 min** (aligned with the hint cooldown, so it does not scare casual players).