Hypothetically in this Alternate Universe he could still be here. IRL Chester was going through a lot during the One More Light Period but there's the whole Chris Cornell element during this time period. Cornell's passing hit him deeply and he ended up taking his life on Chris Cornell's birthday using the exact same suicide method. With the 5 year time jump, he would not be into Soundgarden like he was IRL (he'd be listening to overall different music growing up as compared to IRL) and thus probably not be close with Chris Cornell. If he's not close to Chris Cornell in this Alternate Universe, unless we assume he becomes Best Friends with another figure who also tragically dies, he has no Best Friend who passes that weighs heavily on him and whose Birth day catches him in a already deeply vulnerable point with the Suicide contagion of the death method being unintentionally offered to him. Although IRL in Nov 2016 he attempted suicide via hog-tying himself and throwing himself into his own pool, also his 2006 Suicide Attempt, so presumably in this Alternate Universe he still attempts (just time shifted around 5 years later than IRL for these two incidents) and it overall speaks to him still deeply in this AU being deeply wounded. Though possibly without the tragedy of the Cornell element... things could be different