Yeah, that's exactly right, if you look at the Task initialiser you'll find an annotation called @_inheritActorContext. That means that the closure you pass into the initialiser is isolated the current actor context – and since you annotated your class with @MainActor, that actor context is the main actor. Furthermore, since the annotation is on the whole class, you value property is also isolated to the main actor, which is why you don't need to mark await when accessing it – both the closure inside the Task initialiser and the property are isolated to the main actor.
However, if you look at Task.detached, you'll see that there isn't that @_inheritActorContext annotation, meaning that the closure that you pass into the parameter isn't isolated to the main actor, unlike your value property – which is why you'd need to mark an await when accessing it.