Okay I've been seeing a lot of people talking about Viktor's characterization as a loner on this website and I don't think most people are getting it quite right. I see posts talking about assumptions of intelligent characters as being unemotional loners and about how he was so isolated because he was disabled and like. People are missing what to me is obvious.
The main reason why Viktor is such a loner is this asshole:
certified asshole Corin Reveck
In season 1, before the opening theme, we get shorts of formative experiences in the main character's childhoods. If the main reason for Viktor being a loner was because he was bullied or at least excluded from playing with other kids, that would have been really easy to show. It's not like Arcane shies away from kids being mean to other kids -- look at what happened to Powder! But there's really none of that going on. He's playing away from the other kids but when he makes eye contact with Sky they seem more curious about each other than anything else. He might have been excluded but it's implied that this is not a permanent state.
But, instead of going to play with the other kids, he meets Doctor Corin Reveck and his seeming pet, Rio. Upon their first meeting, Reveck specifically flatters Viktor a lot, telling him that the reason he's alone is because he's smart, and lets him help caring for the cool exotic pet. For a little kid, this seems like a great deal... until it isn't. The pet is being cared for to be tortured, and Viktor realizes that he's only extending the creature's suffering, and he was taken advantage of to create this state of affairs.
Specifically, this creates the link in his mind that positive attention leads to being exploited. Not only does his disability lead to him being excluded, but things about that may lead him to inclusion only lead to bad things for him, too. Not only is he physically vulnerable, but his talents are also a vulnerability. This creates a lose/lose situation socially, so why participate at all?
And because this exploitation is such a normalized idea of what relationships are like for him, he keeps going back to Reveck, and allows himself to continue to be exploited, especially when he's in a vulnerable state -- he's just reverting to what he knows from childhood, that the good parts of him are a resource to be used. That's the obsession with legacy, yet at the same time he can't let himself be known to the public. Positive attention has been poisoned for him. He desperately wants it but doesn't know how to get it in a way that won't harm him. Jayce's love is what resolves this in the end.