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/handlers_user.go

@@ -8,6 +8,7 @@ import (
 	"github.com/google/uuid"
 
 	"scrabble/backend/internal/engine"
+	"scrabble/backend/internal/gamelimits"
 )
 
 // The /api/v1/user/* endpoints require X-User-ID (RequireUserID middleware). The
@@ -189,13 +190,15 @@ func (s *Server) handleEnqueue(c *gin.Context) {
 	if !s.ensureVariantAllowed(c, uid, variant.String()) {
 		return
 	}
-	if !s.ensureUnderGameLimit(c, uid) {
-		return
-	}
+	kind := gamelimits.KindRandom
 	enter := s.matchmaker.Enqueue
 	if req.VsAI {
+		kind = gamelimits.KindVsAI
 		enter = s.matchmaker.StartVsAI
 	}
+	if !s.ensureUnderGameLimit(c, uid, kind) {
+		return
+	}
 	res, err := enter(c.Request.Context(), uid, variant, req.MultipleWordsPerTurn)
 	if err != nil {
 		s.abortErr(c, err)