She made him kill not so innocent people. Killing innocents he started on his own.
Foltest was not only reacting on personal insult, he was also reacting on possible rebellion
Just finished the dlc. and would like to make an in-depth analysis. So here goes.
If one thinks rationally and realistically about the nuance of this whole fiasco, then killing Syanna and letting Detlaff go should indeed be the best course of action. This requires understanding of each main character in this story.
Geralt is a very intelligent person in the books and more so in my playthrough, while also being a superhuman with more understanding of monsters than most. Moreover, he has a special dynamic with powerful individuals that is able to significantly alter the fate of nations. This makes him a formidable ally, or foe. He should be able to see right away that Anna Henrietta's so-called "contract" is in fact a murky political affair, and the Dutchess is probably the most underestimated character in the whole game.
During the first half of the story, Anarietta at least had the right intentions, even personally helping Geralt with his investigation. But as soon as she began to suspect Syanna, the nature of the matter changed, and so was Anna's true nature revealed. She likes being in a position of power, but she also cannot let go of her guilty conscience. I see many people here blame her for putting her sister before thousands of innocent lives. To me this has very little to do with sisterly love and everything to do with the game of court politics that was underfoot. To royalty like Anarietta, it is not the Beast that threatens her position of power, it's Syanna. And yes, I believe Anna knew her sister was behind it all the moment she began to suspect her, but she couldn't admit it since it places her in a position of weakness. Later when vampires began to attack the city, the guards inform her that the people want her to bring Syanna to justice, so we know that somehow the public became aware of Syanna's trecherous deeds. She couldn't comply because deep down she knows the whole mess started because she abandoned Syanna to secure her throne. In other words, Anna needs Syanna dead, but she cannot be the one advocating for it. She needs to feign the complete opposite and have someone else to take the blame. This is why she placed her sister in the Fairytale world as a gamble. If nothing occurs then she became the benevolent protector of her dear sis and (at least in her mind) they might call it even after the dust has settled. However, if by chance desperate individuals such as Detlaff or Geralt manages to get Syanna out, then it most likely becomes a lose-lose situation without involving her directly. If the Beast kills Syanna for her betrayal then Geralt kills the Beast like all those other righteous knight errants, it all plays right into her hands.
On the surface, she might seem to want the first option (i.e. to protect her sis), but deep down she prefers the second outcome (i.e. both Syanna and Detlaff dead). This way it would all be a great tragedy WITHOUT affecting her throne and thus the stability of the realm. When you and Regis went to search the fairytale book that Syanna is essentially imprisoned in, somehow no one was guarding the whole place, and there were no bodies laying around either, I believe this is why.
But here's the catch. She miscalculated two crucial pieces on the board: Syanna and Geralt. How could she be wrong about her sister, shouldn't they know each other best? And what's so important about Geralt? He seemed to be pushed around by her highness ever since he came to Toussaint. This is where a third party comes in.
Higher vampires are, in short, a force of nature best to stay far away from. We have learned through the Tesha Mutna quest that they like treating humans as inferior beings and their unpredictability is off the charts. Even Regis, the most decent of the bunch, outright claims that "to rob you [humans] of life is just plain easy." So, if a human directly seeks out such beings for help, then they are inviting themselves, alongwith everyone involved in the matter, into death's jaws. This is the reality for Syanna, and later for Geralt if he chooses to see the unseen elder. Only the most naive would believe that Syanna didn't know there would be heavy collateral damage for her scheme to success. She was playing with the flame of death and she always knew, because the only way to beat her sister is to truly get everything out of control. This is her final gamble, so that she could either kill Anna or at least make her suffer as she did. This is exactly what would play out unless Geralt somehow make Syanna change her mind (true fairytale that is).Anarietta was essentially too swayed by her own guilty conscience to see the truth - that her own sister has gone all-out just to ruin her.
Finally, we go back to Geralt. How can he get out of this mire? One unchanging rule of the Witcher universe is that by killing monsters, one only attracts more monsters. Geralt's only true friend here is Regis. The one who willingly sacrificed his life to protect Geralt and Yennefer. If Geralt renounced Regis' advice and opt to seek some unstable momentary alliances, then he truly deserved to fail. This is a vampire issue and Regis, he one true friend in all this, knows the most about vampires. Anarietta, Syanna, Dettlaff, the unseen elder and all the other powerful individuals only think of using Geralt to their own gains, only Regis is genuinely helping him. So please do listen to Regis.
As we said before, the Dutchess is trapped by guilt, but deep down she does want to kill two birds with one stone, casualties can come later. A smart Geralt would know that killing Syanna in fact aligns with Anna's interest, and would ensure Toussiant's stability under her rule. That leads to Dettlaff. I see the most common argument supporting his demise is that Dettlaff is "too dangerous to be left alive". This is like saying nukes are dangerous so we should destroy them all. It only looks good on paper. The simple truth is that nukes are only dangerous if they are used. Dettlaff is a beast pushed into a corner who is in the bargaining phase. But he is simply too powerful to enter the acceptance phase. Therefore, when Anarietta refused his demand to present Syanna in 3 days, the nuke is armed and ready to launch. The cause of this conflict is Anna's miscalculation of her sister's core motives, and Dettlaff is but a tool that no longer wished to be pushed around. Failure to understand this is proof that the player has truly been deceived by the appearance of things.
Ultimately, Geralt must make a decision. Should he hurt the tool or the manipulator? Both Anna and Syanna place their needs above everyone else's. If Geralt does execute Dettlaff, the Dutchess wins, and Regis, the only one he could really rely on, would be forced to kill his own savior and brethern, banished and shunned by all vampires for what seems an eternity. Ultimatley, he would become another one of the Dutchess's lapdog at the cost of causing further suffering to his friend who had already died for him once. Sparing Dettlaff, on the other hand, changes the fate of both humans and vampires. The Dutchess finally learns the painful way the consequences of her unchecked power and selfishness. Toussaint's stability is maintained. Regis is unharmed, and Dettlaff sees a new side of humanity through Geralt. This in turn leads to the hope of coexistence instead of the curse of mutually assured annihilation.
Last but not least, Dandelion is finally useful, for once, that brings true closure.