feat(backend): per-tier, per-kind active-game limits with a guest funnel

Cap a player's simultaneous unfinished games per kind (vs_ai, random,
friends) with independent guest and durable-account tiers, held in a new
single-row backend.config table (-1 = unlimited) behind an in-memory cache
and editable live in the admin console (/_gm/limits). Each game is tagged
with games.game_kind on creation.

This replaces the earlier flat MaxActiveQuickGames=10 combined cap: the
per-tier/kind config is the single mechanism, enforced at the same handler
gate (ensureUnderGameLimit by kind on lobby/enqueue) plus the durable
friends cap in CreateInvitation. game.Service.AtGameLimit only resolves the
tier and counts; the limit policy stays at the request edge.

Guests are now refused friend requests, friend-code redemption,
befriend-in-game and invitation creation outright (403 guest_forbidden) --
previously only the UI hid these.

Admin: a kind column in both game lists and the config editor.

Defaults: guest 1 vs_ai / 1 random / 0 friends; durable 10 / 10 / 10.

backend/internal/postgres/migrations/00014_guest_limits.sql

@@ -0,0 +1,36 @@
+-- Guest-limit foundation (E8): tag each game with its kind so the per-tier, per-kind active-game
+-- limits are enforceable, and add the single-row config that holds those limits (tuned in the admin,
+-- no release). It replaces the old hardcoded MaxActiveQuickGames=10 combined cap with a per-tier,
+-- per-kind config. game_kind: 0=unknown (pre-E8 games, never gated), 1=vs_ai, 2=random, 3=friends —
+-- set on creation. The limits are smallint with -1 = unlimited; a guest defaults to 1 vs_ai + 1
+-- random (friends 0, moot — the guest gate blocks friend games), a durable account to 10 per kind
+-- (the old cap, now per kind). Additive only — applies forward via goose with no data rewrite (no
+-- contour wipe); an image rollback ignores the column + table.
+-- +goose Up
+
+ALTER TABLE backend.games
+    ADD COLUMN game_kind smallint DEFAULT 0 NOT NULL;
+ALTER TABLE backend.games
+    ADD CONSTRAINT games_game_kind_chk CHECK (game_kind >= 0 AND game_kind <= 3);
+
+CREATE TABLE backend.config (
+    only_row boolean DEFAULT true NOT NULL,
+    guest_vs_ai_limit smallint DEFAULT 1 NOT NULL,
+    guest_random_limit smallint DEFAULT 1 NOT NULL,
+    guest_friends_limit smallint DEFAULT 0 NOT NULL,
+    durable_vs_ai_limit smallint DEFAULT 10 NOT NULL,
+    durable_random_limit smallint DEFAULT 10 NOT NULL,
+    durable_friends_limit smallint DEFAULT 10 NOT NULL,
+    CONSTRAINT config_pkey PRIMARY KEY (only_row),
+    CONSTRAINT config_single_row_chk CHECK (only_row),
+    CONSTRAINT config_limits_chk CHECK (
+        guest_vs_ai_limit >= -1 AND guest_random_limit >= -1 AND guest_friends_limit >= -1 AND
+        durable_vs_ai_limit >= -1 AND durable_random_limit >= -1 AND durable_friends_limit >= -1)
+);
+
+INSERT INTO backend.config (only_row) VALUES (true);
+
+-- +goose Down
+
+DROP TABLE backend.config;
+ALTER TABLE backend.games DROP COLUMN game_kind;