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/server/server.go

@@ -25,6 +25,7 @@ import (
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/feedback"
 	"scrabble/backend/internal/game"
+	"scrabble/backend/internal/gamelimits"
 	"scrabble/backend/internal/link"
 	"scrabble/backend/internal/lobby"
 	"scrabble/backend/internal/notify"
@@ -100,6 +101,10 @@ type Deps struct {
 	// console routes are registered when the wallet surface lands. A nil Payments
 	// omits them.
 	Payments *payments.Service
+	// GameLimits is the per-tier, per-kind active-game limit config, cached in memory. The
+	// game domain reads it through game.Service (SetGameLimits) for the new-game gate; the admin
+	// console reads and edits it here. A nil GameLimits omits the limits console section.
+	GameLimits *gamelimits.Service
 	// Notifier publishes live-event intents — here the banner-eligibility re-poll
 	// signal the banner/hint/role console actions emit. A nil Notifier discards
 	// them (notify.Nop).
@@ -140,6 +145,7 @@ type Server struct {
 	banview     *banview.View
 	ads         *ads.Service
 	payments    *payments.Service
+	gamelimits  *gamelimits.Service
 	robokassa   robokassa.Config
 	notifier    notify.Publisher
 	console     *adminconsole.Renderer
@@ -194,6 +200,7 @@ func New(addr string, deps Deps) *Server {
 		banview:       deps.BanView,
 		ads:           deps.Ads,
 		payments:      deps.Payments,
+		gamelimits:    deps.GameLimits,
 		robokassa:     deps.Robokassa,
 		notifier:      notifier,
 		renderer:      deps.Renderer,