I mean, let's be honest, the creature types in the MM dont make much sense.
Construct should be a subtype, like:
Flesh Golem, Undead (construct)
Same thing for ''monstrosities''. If they the creature breeds true and have a natural place in the (fantasy) natural order, they should be beast, not ''monstrosities''. It's like saying some types of dogs or vegetables arent an animal or plant because they were bred by science at first. Monstrosities should be for creature outside the natural order, a one off of evolution created by magic, such as yuan-ti anathema.