Vertin is a very emotionless character
but that doesn't mean she's entirely void of empathy or care. She's just kind of a monotone person, and we can see from Chapter 3 that she's always been this way even when she was a child. In all the scenes she's in she's got a pretty flat and even tone, and doesn't sound as if she has any real dislike of other people.
Particularly it's when she's with Sonetto who's so different from her in every aspect, that we see that Vertin despite her need for freedom and to explore the outside world doesn't hold others in contempt for having different aspirations than her.
Vertin's not unaware of how hard it would be for someone to shake off the hold The Foundation has on them if they've lived their entire lives being told what to do and what to think by The Foundation. And while Vertin was also just like every other child who was brought in at a young age, despite this she still holds an insatiable curiosity for the outside world.
So instead of trying to change other people's minds by forcing them to go along with her plans, or turning her back on them, she shows them the parts of the world that drives her to keep going. She shares the parts of the world that pushes her to keep going with other people in the hope that it just inspires them to join her, and nothing more.
And even though Vertin and Sonetto have very different opinions and views about The Foundation, we can see even in the earlier chapters when they're partners that Vertin hasn't stopped trying to bring others over to her side by simply showing them the outside world.
Vertin's care for other people is so strong that you can even see it in other parts of the game, such as the actual game mechanics for the game. I already mentioned on my other blog about how the Resonate game mechanic is a reflection of how Vertin impacts the characters in the suitcase, and I think it's pretty cool how they've managed to put so much of Vertin in the game even if she's not technically a playable character.
Whenever you "bond" with a character, the things they say are directly towards Vertin and not really "you" the player. There's a clear wall between the players and Vertin in terms of even the character interactions, and that's simply because the devs REALLY want you to know that this game is about Vertin trying to inspire people to come to her side on their own.
Reverse: 1999's core theme seems to simply be "Keep living for the future" and that's a nice message until you realize just about every character has a reason for why they'd want things to go "back to the way they were before". In the beginning, the games objective seemed pretty simple: Defeat these bad monsters causing the Storm, save Arcanists in each era, repeat. But by Chapter 2 it's pretty clear that Vertin didn't "win" in the end.
She managed to save some Arcanists, but she still lost people in the process and had no way of really saving those people's loved ones from the Storm. It's a bittersweet ending where Vertin has to ask these random strangers who have probably never interacted before they met her that day to say goodbye to everything they've ever loved.
So then ultimately what can Vertin do besides shelter a few people from The Storm? To her it is worth it to save even a few people if she can, because while she can't save their loved ones from a fate of being erased from existence, she can give them a chance to keep going forward "To the next era".