However the shot of him watching the Tantive IV jump to hyperspace destroys the continuity - how could Leia pretend not to be part of the rebellion when her ship had just undocked and flew out of a battle with her crew knowing that Vader witnessed them??
At the beginning of ANH, the Tantive was already shooting/being shot at by the Star Destroyer. They all knew, Leia was just desperate and made something up. Plus, they could’ve been flying a few days or so, so she could just have been feigning ignorance to the events of the previous battle, as if she’d just recently been picked up.