Couple things worth mentioning here, first that as someone already said, Esau actually despised his birthright. So when I read the story, I realize that when Esau is trading away his birthright, it is an act of intentional belittlement of it. He knows exactly what it is, but he wants to act like he doesn't need it and it's worth less to him than the pottage. So when it turns out he can't back out of it later, he should have foreseen that.
Jacob for his part has to run away from home for and gets deceived/exploited by Laban, who takes advantage as much as he can of being the head of that household. After fourteen years it is Jacob trying to escape under cover of night and Laban goes chasing after him trying to still get more, so Jacob has to pay him off one more time just to get freedom to go home. And after that, Esau is the one who wants to be friendly when he returns, while Jacob is still afraid of receiving some kind of vengeance for what he did after all that time.
In the end, Edom receives its own lands around mount Seir and was its own nation for a while. But it wasn't the birthright that he would have had as the firstborn. But it just shows how his actions were able to make more difference, despite having the fortune of being the first twin to be born, he ended up receiving less inheritance due to his own actions.
And I wouldn't let the talmudic jews bother you, they are so confused about things it will be a rude awakening to them when reality finally sets in.