You specifically unlock the True Ending by doing the mission where you break Kokoro out of jail (though you also need to do the archives and train missions to unlock that in the first place), the other 9 DLC missions are just for auxiliary unlocks (e.g. the arms dealer Wheelghost boss unlocks the improved Picozi Portable variants) and extra lore.
My philosophy is that "it's the journey, not the destination" when it comes to storytelling, so I count all the extra stuff that happens on the path to unlocking the True Ending (e.g. clarification on the Puppet Master's plan, Yuuka's motivations, new true final boss) as part of it. The extended cutscene is just a little extra cherry on top.