It's not true that Japan thought they had a "right" to demand anything. Negotiating terms of surrender goes back to the American Revolution
There is a difference between "negotiating a surrender" and "dictating a cease fire".
And it can be seen quite clearly in that they outright rejected Potsdam, and refuse to consider or discuss it.
If they had honestly been willing to surrender, then at that time they would have opened a dialogue with the Allies. Either directly, or indirectly through a third party. But they did none of that, they openly and publicly dismissed it, even using the word "Mokusatsu", which normally translates to "kill with silence" (but also "treat with silent contempt").
That is because they felt they still had the upper hand in the war. That they were the stronger nation, and had the right and power to dictate terms. And not for a surrender, but an armistice to stop the fighting.
And remember, even Ambassador Soto was urging them constantly to "get serious" about ending the war, before it was too late. We actually have three records of all of their dispatches back and forth. Both those translated via Magic, those from Venona, then again from the Japanese archives themselves.
Japanese Peace feelers in the Soviet Union
www.nuclearfiles.org
I suggest anybody that wants to know how the final two months of the war were from the Japanese perspective read those dispatches.
As you already know, the thinking of the Soviet authorities is realistic. It is difficult to move them with abstractions, to say nothing about the futility of trying to get them to consent to persuasion with phrases beautiful but somewhat remote from the facts and empty in content. In fact, with reference to your proposal in telegram No. 853, Molotov does not show the least interest. And again, in his refusal he gave a very similar answer. If indeed our country is pressed by the necessity of terminating the war, we ourselves must first of all firmly to terminate the war. Without this resolution, an attempt to sound out the intentions of the Soviet Union will result in no benefit. In these days, with the enemy air raids accelerated and intensified, is there any meaning in showing that our country has reserve strength for a war of resistance, or in sacrificing the lives of hundreds of thousands of conscripts and millions of other innocent residents of cities and metropolitan areas?
Dispatch from Ambassador Soto to Foreign Minister Togo, 12 July 1945
No, the Big Six still had it in their minds that they could and would win the war, and had no intention of ending the war unless it was in their favor. And the Allied Powers would never have accepted that.
I find it fascinating that even today, people constantly try to "Monday morning quarterback" the negotiations, and say that Japan thought the Soviets were going to help them negotiate a peace. Here we have their own Ambassador telling them that would not happen, way back on 12 July. He knew the reality of it, and over and over tried to tell Tokyo that it would never happen unless Japan was ready to give major concessions. That only a surrender and not an armistice would end the war.
There is a reason why I constantly encourage people to go to the source documents, and not simply rely upon what others say. Those original documents give a direct peek into exactly was going on, unshaded and without spin. Japan had absolutely no idea we were "reading their mail", and what we see in the Soto-Togo messages was a lot of frustration, and demands to make the Soviets see things the way Japan wanted them to, and to do what they asked.