Chayei Sara Short Essay

What’s the connection between Chayei Sara and the rest of the parsha.
Can read it ויהיו חיי, שרה meaning that the chiyus for the world came from her. Was all due to her.
That is why it says chayei Sara and then goes on to speak about other things, her burial Eliezer getting Rivka for Yitschak etc because that is really her chiyus. Essentially it is her legacy.