The motives for Nilfgaard moving in on Cintra are multifaceted. The TV show makes it sound as though destiny was defied, so fate would have its revenge.
However, in the books
Duny, who marries Pavetta, is Emhyr, Emperor of NIlfgaard, the White Flame Who Dances on the Corpses of His Enemies. He becomes aware of Ithlinne's Prophecy, and his daughter Ciri is key. He fakes his death with the intention of preserving Pavetta, but she tragically dies anyway.
Calanthe isn't gonna give up her granddaughter to a "stranger," so he wages war to get her back. Only known to a select few like Geralt, Emhyr intends to marry and impregnate his own daughter, as the prophecy speaks of a Child of Elder Blood.
Emhyr then recruits Vilgefortz, one of the most powerful sorcerers in the Council of Sorcerers, to stage the Thanedd coup to prevent their interfering with Nilfgaard's assault on the Northern Kingdoms after the Second Battle of Sodden Hill. Vilgefortz then learns of Ithlinne's Prophecy, and designs to abduct Ciri himself. But because he is a raging misogynist, he intends to impregnate Ciri by injection, and do some magic stuff to take the Power as a result.
Yall will find out about Rience and Bonnart and Stefan Skellen next season.
I bet that book stuff will come into play in show too once things start to evolve. Too big things for motives to be ignored.