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/adminconsole/templates/layout.gohtml

@@ -15,6 +15,7 @@
     <a href="/_gm/"{{if eq .ActiveNav "dashboard"}} class="active"{{end}}>Dashboard</a>
     <a href="/_gm/users"{{if eq .ActiveNav "users"}} class="active"{{end}}>Users</a>
     <a href="/_gm/games"{{if eq .ActiveNav "games"}} class="active"{{end}}>Games</a>
+    <a href="/_gm/limits"{{if eq .ActiveNav "limits"}} class="active"{{end}}>Limits</a>
     <a href="/_gm/complaints"{{if eq .ActiveNav "complaints"}} class="active"{{end}}>Complaints</a>
     <a href="/_gm/feedback"{{if eq .ActiveNav "feedback"}} class="active"{{end}}>Feedback</a>
     <a href="/_gm/messages"{{if eq .ActiveNav "messages"}} class="active"{{end}}>Messages</a>

backend/internal/adminconsole/templates/pages/games.gohtml

@@ -8,11 +8,11 @@
 <a href="/_gm/games?status=finished"{{if eq .Status "finished"}} class="active"{{end}}>finished</a>
 </nav>
 <table class="list">
-<thead><tr><th>Game</th><th>Variant</th><th>Status</th><th>🤖</th><th class="num">Players</th><th>Updated</th></tr></thead>
+<thead><tr><th>Game</th><th>Variant</th><th>Kind</th><th>Status</th><th>🤖</th><th class="num">Players</th><th>Updated</th></tr></thead>
 <tbody>
 {{range .Items}}
-<tr><td><a href="/_gm/games/{{.ID}}">{{.ID}}</a></td><td>{{.Variant}}</td><td>{{.Status}}</td><td>{{if .VsAI}}🤖{{end}}</td><td class="num">{{.Players}}</td><td>{{.UpdatedAt}}</td></tr>
-{{else}}<tr><td colspan="6"><span class="note">no games</span></td></tr>{{end}}
+<tr><td><a href="/_gm/games/{{.ID}}">{{.ID}}</a></td><td>{{.Variant}}</td><td>{{.Kind}}</td><td>{{.Status}}</td><td>{{if .VsAI}}🤖{{end}}</td><td class="num">{{.Players}}</td><td>{{.UpdatedAt}}</td></tr>
+{{else}}<tr><td colspan="7"><span class="note">no games</span></td></tr>{{end}}
 </tbody>
 </table>
 <nav class="pager">

backend/internal/adminconsole/templates/pages/limits.gohtml

@@ -0,0 +1,19 @@
+{{define "content" -}}
+<h1>Active-game limits</h1>
+{{with .Data}}
+<p class="note">Per-tier, per-kind caps on a player's simultaneous unfinished games. <strong>-1</strong> = unlimited, <strong>0</strong> = the kind is blocked, a positive number caps concurrent games of that kind. Guests are additionally blocked from friend games outright. Changes apply immediately (no redeploy); games already in progress are never affected.</p>
+<section class="panel">
+<form class="form col" method="post" action="/_gm/limits">
+<h2>Guest</h2>
+<label>vs AI <input type="number" name="guest_vs_ai" min="-1" value="{{.GuestVsAI}}" required></label>
+<label>Random <input type="number" name="guest_random" min="-1" value="{{.GuestRandom}}" required></label>
+<label>Friends <input type="number" name="guest_friends" min="-1" value="{{.GuestFriends}}" required></label>
+<h2>Durable account</h2>
+<label>vs AI <input type="number" name="durable_vs_ai" min="-1" value="{{.DurableVsAI}}" required></label>
+<label>Random <input type="number" name="durable_random" min="-1" value="{{.DurableRandom}}" required></label>
+<label>Friends <input type="number" name="durable_friends" min="-1" value="{{.DurableFriends}}" required></label>
+<div><button type="submit">Save</button></div>
+</form>
+</section>
+{{end}}
+{{- end}}

backend/internal/adminconsole/templates/pages/user_detail.gohtml

@@ -211,11 +211,11 @@
 {{end}}
 <section class="panel"><h2>Games</h2>
 <table class="list">
-<thead><tr><th>Game</th><th>Variant</th><th>Status</th><th class="num">Players</th><th>Updated</th></tr></thead>
+<thead><tr><th>Game</th><th>Variant</th><th>Kind</th><th>Status</th><th class="num">Players</th><th>Updated</th></tr></thead>
 <tbody>
 {{range .Games}}
-<tr><td><a href="/_gm/games/{{.ID}}">{{.ID}}</a></td><td>{{.Variant}}</td><td>{{.Status}}</td><td class="num">{{.Players}}</td><td>{{.UpdatedAt}}</td></tr>
-{{else}}<tr><td colspan="5"><span class="note">no games</span></td></tr>{{end}}
+<tr><td><a href="/_gm/games/{{.ID}}">{{.ID}}</a></td><td>{{.Variant}}</td><td>{{.Kind}}</td><td>{{.Status}}</td><td class="num">{{.Players}}</td><td>{{.UpdatedAt}}</td></tr>
+{{else}}<tr><td colspan="6"><span class="note">no games</span></td></tr>{{end}}
 </tbody>
 </table>
 </section>

backend/internal/adminconsole/views.go

@@ -312,6 +312,8 @@ type GameRow struct {
 	UpdatedAt string
 	// VsAI marks an honest-AI game (rendered as 🤖 in the list's AI column).
 	VsAI bool
+	// Kind is the game's origin tag label: vs_ai / random / friends / unknown.
+	Kind string
 }
 
 // GamesView is the paginated games list, optionally filtered by status.
@@ -321,6 +323,17 @@ type GamesView struct {
 	Pager  Pager
 }
 
+// GameLimitsView is the per-tier, per-kind active-game limit form: each field is a cap where -1
+// is unlimited, 0 blocks the kind, and a positive value caps concurrent games of that kind.
+type GameLimitsView struct {
+	GuestVsAI      int
+	GuestRandom    int
+	GuestFriends   int
+	DurableVsAI    int
+	DurableRandom  int
+	DurableFriends int
+}
+
 // GameDetailView is one game with its seats.
 type GameDetailView struct {
 	ID          string