IMHO having taken an oath on Carl Sagan’s name and book is more important and serious than swearing on any god/spirit/force/deity (from whatever religion).
I'm Christian and for me, taking an oath on the Bible is the biggest binding I can imagine. I hope Lystrup made her choice as that book is close to her heart and provides her great support to stay true to her oath. I would be disappoined if this were just a marketing move as that would further erode the value of oaths, honesty and ultimately honor.
That means nothing to some people. In which case I’d argue an oath means strictly less than if you have some higher power you feel accountable to. I don’t think anyone thinks - least of all Carl Sagan - that Carl Sagan can hold themselves accountable for broken promises.
In this case it’s being used as a demonstration of values which people don’t necessarily see as having any eternal or cosmic weight. Do they believe the nature of not following these values begets some sort of divine justice? The very fact that they are choosing them seems to imply no - others may choose different values and not fulfill those ones. Do they think such oaths should be rejected?
So for example like oath of fealty vs vow of poverty. The difference is inherently religious and kind of subtle and not explicit in most contexts, plus vows aren't very common anymore. But if you read for example a christian marriage vow next to an oath of office you can clearly see the different intent.
And again the meanings are usually the same in general modern use and the religious rite aspect is probably not very important to many people. But when talking about a specific formal oath or vow you can definitely tell that it's two separate rites.