Fix coords monitor in replays (#29512)

The F3 coords manager is blocked if you're not an admin. This check happened even when playing a replay, where you actually aren't. There's now a check to make sure you are actually server-connected-to-game before running the logic.

Also moved it to a manager because this *shouldn't be a bloody entity system in the first place*.

Content.Client/Entry/EntryPoint.cs

@@ -1,6 +1,7 @@
 using Content.Client.Administration.Managers;
 using Content.Client.Changelog;
 using Content.Client.Chat.Managers;
+using Content.Client.DebugMon;
 using Content.Client.Eui;
 using Content.Client.Fullscreen;
 using Content.Client.GhostKick;
@@ -33,6 +34,7 @@ using Robust.Shared.Configuration;
 using Robust.Shared.ContentPack;
 using Robust.Shared.Prototypes;
 using Robust.Shared.Replays;
+using Robust.Shared.Timing;
 
 namespace Content.Client.Entry
 {
@@ -68,6 +70,7 @@ namespace Content.Client.Entry
         [Dependency] private readonly IReplayLoadManager _replayLoad = default!;
         [Dependency] private readonly ILogManager _logManager = default!;
         [Dependency] private readonly ContentReplayPlaybackManager _replayMan = default!;
+        [Dependency] private readonly DebugMonitorManager _debugMonitorManager = default!;
 
         public override void Init()
         {
@@ -205,5 +208,13 @@ namespace Content.Client.Entry
                 _stateManager.RequestStateChange<MainScreen>();
             }
         }
+
+        public override void Update(ModUpdateLevel level, FrameEventArgs frameEventArgs)
+        {
+            if (level == ModUpdateLevel.FramePreEngine)
+            {
+                _debugMonitorManager.FrameUpdate();
+            }
+        }
     }
 }