One angle I haven't seen discussed much is how vulnerability functions in these stories. A ruthless protagonist often gets sympathy not from their actions but from glimpses of their internal cost. There's this moment in 'The Poppy War' where Rin does something absolutely horrific, but the narrative has already spent so much time showing you the brutal, dehumanizing system that forged her. You don't agree with her, but you understand the machinery that produced her. It's like watching a forest fire and understanding the lightning strike that started it.
The other big trick is contrasting them against something even worse. If the world they're in is so corrupt, so fundamentally broken that mercy is just a weakness to be exploited, then their ruthlessness starts to look like a grim necessity. The 'sympathy' isn't warm and fuzzy; it's more a cold, bleak acceptance that maybe this is the only kind of tool that can fix a world this shattered. You root for them not because you like them, but because you dread the alternative.
Ultimately, I think it hinges on whether the story convinces you their cruelty is a wound, not a personality. When it's a weapon they're forced to wield, it creates a tragic tension. When it's just who they are, that's when you lose me.