Most directly, since imaginability, 'can' and 'must' are traditional modes, Modal Realism asserts what you are considering. But it does not determine an actual philosophical position. The question remains open what range of modes you want to take seriously as a point of reference and which mode you mean to consider 'real'.
Your two italicized conditions together constitute a 'mode' in the sense of modal logic. It is the mode of 'actuality'. The two boundaries are not really different, except for being opposite ways of putting the same thing. What we cannot say must not exist is exactly what could exist. But clearly even this is a point on a continuum. We do not mean these things are real in the sense of existing right here and now. Tomorrow morning is real in some senses, and not in others. So there is, in fact, a range of modes around 'the actual' that are not the same.
The notion of what can be imagined is another mode. We can imagine exactly what doesn't break down our ability to imagine it.
A concept of modal realism is the assertion that some two points on the manifold of modes are in fact the same, and the space between them is imaginary or misleading. Two extreme forms state that the whole range doesn't exist. That imagination is somehow physically determined and fixed in scope, having to accord in some way with our physical world, at one end, or that everything that we can even mention exists in the same way as the ground we stand on, at the other.
Imagined possibility in the sense of Kripke is a vague middle space in the realm of modes.
We can move up, bracing in our imagination with constraints and talk about what 'should' exist 'given...'. You can imagine the five ton ants from THEM!, but in reality those could not exist. They are not realistic: they should not exist given the rules of Newtonian physics. Their exoskeletons would not take the weight, they would all crack open and die before reaching this size, or their skins would have to be so thick and the poor things could get no oxygen. At the same time, we can predict a planet just half the size of earth, and be pretty sure this is realistic, even if we can't go out and find one. (And you can move 'up' in slightly different directions, imagining say the facts of physics are facts, and the facts of psychology or chemistry are not. So this is not really just a spectrum, but it is largely so.)
There are people who admit worlds as 'possible' only if they satisfy the requirements of all know and future science. If you add history, observed and unobserved, and you accept determinism, you get the position where this is the only possible world.
We can also move down and talk about what 'would' exist 'if only...'. Things can be considered hypothetically or wished for which may not make sense. For example, When mathematicians consider something like the hairy ball without a cowlick, it is ambiguous to what degree they are actually imagining it, since it is actually inherently self-contradictory. But they are doing something. They are processing it in some way despite its potential (in this case provable) nonexistence. For the duration of the proof of its own inconceivability, it is in some way 'real', in order that we can do the mental actions to it that lead us into the contradiction... And it would be equally so whether we found that contradiction or not.
There are people who demand all of these things are also real. David Lewis has tried to rationalize this position. Meinong has gone way beyond it. Then we have to worry about what modal point they chose to imagine they meant by real. I am not going home to purple unicorns this evening...