Sebastian tries to reason through the extraordinary situation. Olivia proposes a formal betrothal and they go together to the chapel.
Sebastian is alone in the garden trying to make sense of what has happened. He checks the evidence: the air is real, the sun is real, the pearl Olivia gave him is solid in his hand. He is not mad, even though the situation is extraordinary. He wonders briefly where Antonio is and why he cannot be found, then moves on.
Olivia arrives with a priest. She has a proposal: she is afraid Sebastian will change his mind, that whatever confusion made Cesario behave so strangely will return. She wants him to commit formally, before a witness, in a ceremony that will bind them properly before anything can go wrong. She asks him to betroth himself to her here, in the chapel nearby.
Sebastian says yes. They go together.
Sebastian's soliloquy is the scene's most important contribution to the play. He works through the extraordinary rationally: "This is the air; that is the glorious sun; / This pearl she gave me, I do feel't and see't." He checks each piece of evidence and concludes that the world is as solid as it appears. Since the world is solid, he is not mad. Since he is not mad, the extraordinary thing that is happening must be real.
This approach, checking evidence and trusting what can be directly observed, is the opposite of how almost every other character handles their situation. Orsino imagines; Olivia projects; Malvolio fantasises. Sebastian looks. His straightforwardness is not stupidity; it is the most rational response available to him, and it is this quality that makes him the instrument of resolution rather than further confusion.
The thought of Antonio is handled quickly: "Where's Antonio, then? / I could not find him at the Elephant." The brevity is telling. Antonio, who has risked his life to follow Sebastian to Illyria and whose devotion is the play's most intense, is here a brief afterthought. Sebastian needs someone to consult about his surprising new situation; Antonio would be useful for that purpose. The emotional weight Antonio has invested is not returned in this scene.
Olivia's proposal is the boldest act of the play. She is a countess. She initiates. She takes the traditionally male role of proposer and does so without embarrassment, justifying the urgency with a practical reason, she does not want to lose him, but proceeding from genuine feeling. This mirrors Viola's transgression of gender norms in the other direction: both women in the play act with more directness and decision than the men around them.