fix #31963: Stopped climbing movent while in containers (#32033)

* hack to resolve offset issues while in locker

* moved movment cancel from lerp to init

* Added DoAfter canceling for buckling and stowing

* changed container event & removed inventory check from climb initation

* resolved integration test fail

* style

---------

Co-authored-by: Milon <milonpl.git@proton.me>

Content.Shared/Climbing/Components/ClimbingComponent.cs

@@ -1,3 +1,4 @@
+using Content.Shared.DoAfter;
 using System.Numerics;
 using Robust.Shared.GameStates;
 using Robust.Shared.Serialization.TypeSerializers.Implementations.Custom;
@@ -25,6 +26,12 @@ public sealed partial class ClimbingComponent : Component
     [AutoNetworkedField, DataField]
     public bool IsClimbing;
 
+    /// <summary>
+    /// The Climbing DoAfter.
+    /// </summary>
+    [DataField]
+    public DoAfterId? DoAfter;
+
     /// <summary>
     /// Whether the owner is being moved onto the climbed entity.
     /// </summary>