diplomail (Stage B): admin/owner sends + lifecycle hooks

Item 7 of the spec wants game-state and membership-state changes to
land as durable inbox entries the affected players can re-read after
the fact — push alone times out of the 5-minute ring buffer. Stage B
adds the admin-kind send matrix (owner-driven via /user, site-admin
driven via /admin) plus the lobby lifecycle hooks: paused / cancelled
emit a broadcast system mail to active members, kick / ban emit a
single-recipient system mail to the affected user (which they keep
read access to even after the membership row is revoked, per item 8).

Migration relaxes diplomail_messages_kind_sender_chk so an owner
sending kind=admin keeps sender_kind=player; the new
LifecyclePublisher dep on lobby.Service is wired through a thin
adapter in cmd/backend/main, mirroring how lobby's notification
publisher is plumbed today.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/internal/server/router.go

@@ -76,6 +76,7 @@ type RouterDependencies struct {
 	AdminRuntimes *AdminRuntimesHandlers
 	AdminEngineVersions *AdminEngineVersionsHandlers
 	AdminMail *AdminMailHandlers
+	AdminDiplomail *AdminDiplomailHandlers
 	AdminNotifications *AdminNotificationsHandlers
 	AdminGeo *AdminGeoHandlers
 	InternalSessions *InternalSessionsHandlers
@@ -165,7 +166,7 @@ func withDefaultHandlers(deps RouterDependencies) RouterDependencies {
 		deps.UserGames = NewUserGamesHandlers(nil, nil, deps.Logger)
 	}
 	if deps.UserMail == nil {
-		deps.UserMail = NewUserMailHandlers(nil, deps.Logger)
+		deps.UserMail = NewUserMailHandlers(nil, nil, nil, deps.Logger)
 	}
 	if deps.UserSessions == nil {
 		deps.UserSessions = NewUserSessionsHandlers(nil, deps.Logger)
@@ -188,6 +189,9 @@ func withDefaultHandlers(deps RouterDependencies) RouterDependencies {
 	if deps.AdminMail == nil {
 		deps.AdminMail = NewAdminMailHandlers(nil, deps.Logger)
 	}
+	if deps.AdminDiplomail == nil {
+		deps.AdminDiplomail = NewAdminDiplomailHandlers(nil, deps.Logger)
+	}
 	if deps.AdminNotifications == nil {
 		deps.AdminNotifications = NewAdminNotificationsHandlers(nil, deps.Logger)
 	}
@@ -274,6 +278,7 @@ func registerUserRoutes(router *gin.Engine, instruments *metrics.Instruments, de
 
 	userMail := userGames.Group("/:game_id/mail")
 	userMail.POST("/messages", deps.UserMail.SendPersonal())
+	userMail.POST("/admin", deps.UserMail.SendAdmin())
 	userMail.GET("/messages/:message_id", deps.UserMail.Get())
 	userMail.POST("/messages/:message_id/read", deps.UserMail.MarkRead())
 	userMail.DELETE("/messages/:message_id", deps.UserMail.Delete())
@@ -314,6 +319,7 @@ func registerAdminRoutes(router *gin.Engine, instruments *metrics.Instruments, d
 	games.POST("/:game_id/force-start", deps.AdminGames.ForceStart())
 	games.POST("/:game_id/force-stop", deps.AdminGames.ForceStop())
 	games.POST("/:game_id/ban-member", deps.AdminGames.BanMember())
+	games.POST("/:game_id/mail", deps.AdminDiplomail.Send())
 
 	runtimes := group.Group("/runtimes")
 	runtimes.GET("/:game_id", deps.AdminRuntimes.Get())