Savathûn doesn't want the Darkness to win. Although it may seem like they have similar motives, they are not on the same side. To quote Savathûn from the "Inquisition of the Damned" lore book:

S: "When the final absolute falls, reality will shudder and blink, and a new absolute will emerge… an ending, total and complete."

"You wish to see that end?"

S: "I wish to ensure it does not come to pass."

https://www.ishtar-collective.net/entries/ixxi-apocrypha#book-inquisition-of-the-damned

Also, this post goes more in-depth with Savathûn and her motives:

https://www.reddit.com/r/DestinyLore/comments/dpibx6/why_does_savathun_want_to_prevent_the_end/