Misc replay related changes (#17102)

Content.Client/Examine/ExamineSystem.cs

@@ -16,6 +16,7 @@ using Robust.Shared.Utility;
 using System.Linq;
 using System.Threading;
 using Content.Shared.Eye.Blinding.Components;
+using Robust.Client;
 using static Content.Shared.Interaction.SharedInteractionSystem;
 using static Robust.Client.UserInterface.Controls.BoxContainer;
 
@@ -28,6 +29,7 @@ namespace Content.Client.Examine
         [Dependency] private readonly IPlayerManager _playerManager = default!;
         [Dependency] private readonly IEyeManager _eyeManager = default!;
         [Dependency] private readonly VerbSystem _verbSystem = default!;
+        [Dependency] private readonly IBaseClient _client = default!;
 
         public const string StyleClassEntityTooltip = "entity-tooltip";
 
@@ -341,10 +343,10 @@ namespace Content.Client.Examine
                 canSeeClearly = false;
 
             OpenTooltip(playerEnt.Value, entity, centeredOnCursor, false, knowTarget: canSeeClearly);
-            if (entity.IsClientSide())
+            if (entity.IsClientSide()
+                || _client.RunLevel == ClientRunLevel.SinglePlayerGame) // i.e. a replay
             {
                 message = GetExamineText(entity, playerEnt);
-
                 UpdateTooltipInfo(playerEnt.Value, entity, message);
             }
             else