Updated the domain model with entities, repos and domain services. Looks good. I think I addressed all the user stories however if I fell short we'll revise as needed.

LibraryApp.Domain/Entities/Shelf.cs

@@ -0,0 +1,44 @@
+namespace LibraryApp.Domain.Entities;
+
+public class Shelf
+{
+    public ShelfId Id { get; private set; }
+    public ShelfName Name { get; private set; }
+    public DateTime? LastCountedAt { get; private set; }
+
+    public Shelf(ShelfName name)
+        : this(new ShelfId(string.Empty), name, null)
+    { }
+
+    public Shelf(ShelfId id, ShelfName name, DateTime? lastCountedAt)
+    {
+        Id = id;
+        Name = name;
+        LastCountedAt = lastCountedAt;
+    }
+
+    public Shelf RecordCount()
+    {
+        LastCountedAt = DateTime.UtcNow;
+        return this;
+    }
+}
+
+public record ShelfId : DbId
+{
+    public ShelfId(string id) : base(id) {}
+}
+
+public record ShelfName
+{
+    public string Name { get; init; }
+
+    public ShelfName(string name)
+    {
+        if(string.IsNullOrWhiteSpace(name))
+        {
+            throw new ArgumentException("Shelf name cannot be empty.");
+        }
+        Name = name;
+    }
+}