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_admin_console.go

@@ -70,6 +70,10 @@ func (s *Server) registerConsole(router *gin.Engine) {
 	gm.POST("/bans/unban", s.consoleUnban)
 	gm.GET("/games", s.consoleGames)
 	gm.GET("/games/:id", s.consoleGameDetail)
+	if s.gamelimits != nil {
+		gm.GET("/limits", s.consoleLimits)
+		gm.POST("/limits", s.consoleUpdateLimits)
+	}
 	gm.GET("/complaints", s.consoleComplaints)
 	gm.GET("/complaints/:id", s.consoleComplaintDetail)
 	gm.POST("/complaints/:id/resolve", s.consoleResolveComplaint)
@@ -1244,7 +1248,7 @@ func (s *Server) consoleUUID(c *gin.Context, back string) (uuid.UUID, bool) {
 
 // gameRow projects a game summary into its console row.
 func gameRow(g game.Game) adminconsole.GameRow {
-	return adminconsole.GameRow{ID: g.ID.String(), Variant: g.Variant.String(), Status: g.Status, Players: g.Players, UpdatedAt: fmtTime(g.UpdatedAt), VsAI: g.VsAI}
+	return adminconsole.GameRow{ID: g.ID.String(), Variant: g.Variant.String(), Status: g.Status, Players: g.Players, UpdatedAt: fmtTime(g.UpdatedAt), VsAI: g.VsAI, Kind: g.Kind.String()}
 }
 
 // trimForm returns the trimmed value of a posted form field.