To be clear, Hegemony does not involve colonization.
Colonization is only involved in Virgin or pre-warp civilizations (or replacing a civ destroyed by invasion).
Can colonize Virgin worlds
Can't do anything with pre-warp civs
Can't invade any pre warp/warp/other players worlds.
Can Hegemony warp capable and other player systems.
Came here to say this. Hegemony is just a new planet freely joining The Federation. That and colonizing virgin worlds is how they expand in the shows.