If the class won’t be used by third parties and you don’t need an overloaded constructor, don’t write an empty constructor.
But…
Imagine you already shipped the product, and third parties use your class. A few months later there’s a new requirement that makes you add a constructor with an argument.
Now, by doing so, the C# compiler no longer generates a default constructor. If you don’t add an empty constructor explicitly, the third party code will be break.
In my opinion, you should always define empty constructors (one liner) for public classes used by third parties.