[HOTFIX] Admin Menu player jobs (#34545)

update job info on spawn

Content.Server/GameTicking/GameTicker.Spawning.cs

@@ -2,6 +2,7 @@ using System.Globalization;
 using System.Linq;
 using System.Numerics;
 using Content.Server.Administration.Managers;
+using Content.Server.Administration.Systems;
 using Content.Server.GameTicking.Events;
 using Content.Server.Spawners.Components;
 using Content.Server.Speech.Components;
@@ -27,6 +28,7 @@ namespace Content.Server.GameTicking
     {
         [Dependency] private readonly IAdminManager _adminManager = default!;
         [Dependency] private readonly SharedJobSystem _jobs = default!;
+        [Dependency] private readonly AdminSystem _admin = default!;
 
         [ValidatePrototypeId<EntityPrototype>]
         public const string ObserverPrototypeName = "MobObserver";
@@ -233,6 +235,7 @@ namespace Content.Server.GameTicking
 
             _roles.MindAddJobRole(newMind, silent: silent, jobPrototype:jobId);
             var jobName = _jobs.MindTryGetJobName(newMind);
+            _admin.UpdatePlayerList(player);
 
             if (lateJoin && !silent)
             {