It could deepen. Their talk would likely involve a lot of emotions and shared experiences, which would bring them closer. They might become more committed to each other, perhaps even start planning their wedding or a more permanent living arrangement.
They would support each other more. After the battle, they both need someone to lean on. Their conversation could be the start of a stronger bond where they are always there for one another. For example, if Harry has nightmares about the battle, Ginny would be there to comfort him, and vice versa.
The relationship could also become more public. Before the battle, they may have had some moments in private. But after their talk, they might decide to be more open about their relationship in the wizarding community. They could start attending events together more often and show the world that they are a couple, and that love can prevail even after such a dark time.