Salām is more than a routine word; it carries a wish and prayer for peace. Greeting familiar people appropriately can renew goodwill and reduce coldness. It does not by itself settle every disagreement, but it may open an avenue for respectful conversation.
In أَوْلَى النَّاسِ بِاللَّهِ, أَوْلَى is an elative form, and بِاللَّهِ is a prepositional phrase. This expresses special merit or nearness, not a humanly certain verdict on anyone’s final state.
Beginning a difficult conversation with an appropriate greeting can set a better tone, provided the other person’s rights remain respected.