Your antagonist’s motif isn’t the only thing that decides if they’re sympathetic or just plain evil. Something else that’s important is their actions and personality.
A pure evil villain will likely be seen as someone who’s day to day actions upset people. Yes, their grand plans to rule the world upset people, but these are often too large for people to properly process. While ordinary people, who will be most of your consumers, generally have little to no reference to something like genocide. Sure, we know of the actions of world war II, but most people have never experienced something like that. Plus, villains having large plans like that are often seen as being cloche which desensitizes a lot of audience members. This often means that a villain who’s purely evil will also have little subtlety or tact, while someone who’s sympathetic will often be more composed and respectful. One of the best ways to show their personality is how a villain treats their allies or subordinates. A purely evil villain will generally treat their subordinates poorly. This would include something like killing, heavily punishing or humiliating subordinates who make relatively minor mistakes, or merely treating people poorly regardless. A sympathetic antagonist will also often show some sympathy for others. This can be a way to show that deep down the antagonist isn’t so bad, they’re just misguided.
An antagonist’s attitude towards their own plan can also be a good indicator. If they regret any bad actions they take, hesitate, or outright refuse to cross a particular line at some point, it means that they can seem a little bit more sympathetic. Someone who shows some kind of “honour code” shows that they do have some sort of standard. This would be something like an action movie villain who doesn’t kill civilians or unarmed people. In a sports movie, an antagonist who doesn’t cheat or play dirty would make them more sympathetic as well.
How they interact with the protagonist and collateral damage is also a big deal. If someone is focused on just disarming or neutralizing the protagonist, especially in a non-lethal way, they become more sympathetic. On the other hand, someone who doesn’t kill what third parties they have to harm in order to get their revenge on the protagonist is certainly someone who would be considered evil.
It's important to point out here that although you generally have to commit to one side or the other, you are allowed to mix to an extent. What this means is that it's generally best to pick whether your antagonist is either sympathetic or pure evil, but sometimes, especially with the sympathetic antagonist, it's best to give them one or two qualities of the other one in order to stop your story from becoming too cookie cutter or formulaic.
