Since PropertyDrawers are shared between all instances, CreatePropertyGUI() needs to always returns a new VisualElement. Here is a modified version of the custom property drawer that will allow you to edit each value independently.

[CustomPropertyDrawer(typeof(SkillHolderSerialized), true)]
public class SkillHolderSerializedDrawer : PropertyDrawer
{
public override VisualElement CreatePropertyGUI(SerializedProperty property)
{
var container = new VisualElement();

CreateSkillEditor(container, "skill.");

return container;
}
public static void CreateSkillEditor(VisualElement container, string bindingPathPrefix)
{
var uuid = new IntegerField()
{
label = "Uuid",
bindingPath = $"{bindingPathPrefix}{nameof(Skill.uuid)}"
};
container.Add(uuid);

var nameField = new TextField()
{
label = "Skill Name",
bindingPath =$"{bindingPathPrefix}{nameof(Skill.skillName)}"

};
container.Add(nameField);

var descriptionField = new TextField()
{
label = "Skill Description",
bindingPath = $"{bindingPathPrefix}{nameof(Skill.skillDescription)}",
multiline = true
};
container.Add(descriptionField);
}
}