Normally we watch the sun descend, it's dimmed a bit by the atmosphere before dropping below the horizon.
What I'm interested in is how big it would have to be so the atmospheric dimming is sufficient that the point it dips below the horizon is unnoticeable.
External Edit: This is how I understand the question: On Earth the sunset has two phases. In the first phase the sun moves towards the horizon, and its light is dimmed by the shallower angle it makes with the planet and the longer journey through the horizon. The light continues dimming as the angle becomes shallower. The second phase begins when the sun touches the horizon. Usually the atmospheric dimming is mild enough that the outline of the sun can be seen touching the horizon. In phase 2 the sun moves under the horizon the dimming is more pronounced than phase 1 and continues until the sun is no longer visible.
The Asker wants a world where the dimming in phase 1 is so extreme that by the beginning of phase 2, the outline of the sun can no longer be made out in the sky. Maybe it is visible as an indistinct glow or maybe there is no light getting through the atmosphere at all!
(Assume an unaided human observer in an atmosphere suitable for a terrestrial ecosystem, it need not be exactly Earth's atmosphere. When the star is overhead something like 1000W/m^2 like we get on Earth.)
I have no doubt this has to be far bigger than any rocky planet and thus must be some sort of megastructure. (Say, a Dyson Sphere with stars orbiting it.)