How should I deal with tacky alkyd paint on metal stairs?
Curing time for alkyd base paint can vary but I would recommend waiting at least 1 week. Temperature will also affect curing time. If you notice the coating hardening after a week then more time all you need for it to fully cure. If it's still tacky then you might want to research the thinning material a a bit more. Compatibility or mix ratios might be reasons the coating won't cure properly.

Also, be mindful of dust if you decide to blow air onto the stairs. Dust will stick to the coating and once it's on and sticks, it's on for good.