If you're curious about the implementation details of the specific tool that are not explained in its official documentation, you should study directly its source code to find the answer.

But answering your specific question:

Is harness tool equipped with kubectl client tool to perform kubectl apply on kubernetes manifest?

Well, it doesn't have to. Writing a tool which in its code uses a console kubectl client isn't very optimal and doesn't make much sense. For performing exactly the same actions that kubectl does, such tools use Client Libraries. As you can see in the official docs, there is large variety of them, some of them are officialy supported, others are community-maintained, but altogether they support various programming languages.

Of course, you can write an external tool which doesn't use client libraries but implements the API calls and request/response types on its own.