Horton by both skill/readiness and injury ramp probably won't be able to be an unreserved SP at the MLB level. He'd basically never face the order a 3rd time, and you'd probably only plan on 4 IP in a given start. Because of those limitations, I think we'll see multiple contingencies(Rea, Assad, Wicks) before they turn to Horton, which could be never if there aren't (multiple?) other rotation injuries.
But I also think it's likely that as he gets built up, he'll reach a point over the summer where he's banked enough innings that he becomes a relief option(as a MIRP or short reliever) since finishing as a reliever at the big league level won't jeopardize his ramp up for 2026. Plus we know the team prefers to break in pitchers this way. So at the moment I'd say it's unlikely we see Horton as a SP in Chicago this year, but fairly likely that he ends up a meaningful part of the bullpen come July/August.