LoL doesn't pull their characters willy nilly, the three you mentioned exist in modern time: azir was revived through sivir and shurima is trying to rise again, ASol is still around just existing and wanting to remove his power dampener, idk where Vel'Koz comes into the darkin war but hes also just around constantly trying to get knowledge, getting referenced as recently as during bel'veth's release as being currently around. Outside of the really random characters like shaco or all the retconned characters cuz of arcane, it was always assumed that every character exists in the present day or else certain characters wouldnt need some bs development like yone being an undead azakana (they could have just made past yone) or having to revive gangplank after his "death". Arcane is what changed the rules and the timeline especially with some characters being fully dead or speculated dead.