Fix lathe unanchor interaction & general cleanup (#10156)

Content.Server/Lathe/Components/LatheProducingComponent.cs

@@ -1,3 +1,6 @@
+using Content.Shared.Research.Prototypes;
+using Robust.Shared.Serialization.TypeSerializers.Implementations.Custom.Prototype;
+
 namespace Content.Server.Lathe.Components
 {
     /// <summary>
@@ -5,5 +8,17 @@ namespace Content.Server.Lathe.Components
     /// <summary>
     [RegisterComponent]
     public sealed class LatheProducingComponent : Component
-    {}
+    {
+        /// <summary>
+        /// The recipe the lathe is currently producing
+        /// </summary>
+        [DataField("recipe", required:true, customTypeSerializer:typeof(PrototypeIdSerializer<LatheRecipePrototype>))]
+        public string? Recipe;
+
+        /// <summary>
+        /// Remaining production time, in seconds.
+        /// </summary>
+        [DataField("timeRemaining", required: true)]
+        public float TimeRemaining;
+    }
 }