Does that mean that everyone around could actually see the Holy Spirit?
God spoke to Jesus, saying "You are my Son....," an allusion to God's promise to the king in Psalm 2:7. As God's son, Jesus is invested with and will act in accordance with God's power.
Allen & Williamson in their Preaching the Gospels without Blaming the Jews, add:
The words "my beloved in whom I am well pleased" allude to Isaiah 42:1, which describes the servant of Israel witnessing to God's faithfulness and justice. Other resist that witness and cause the servant to suffer. Luke thus shows that Jesus will bring about justice (especially after the apocalypse) by following the path of suffering love.
In Matthew's gospel the voice spoke to the crowd. Is Luke telling us that only Jesus could hear? If the crowds could see the Holy Spirit but not hear the voice, what would did they think? After all, we weren't there but the message conveyed by the voice and the image of the Holy Spirit still affects us.
And our baptism includes us in Christ's community.
Lectio Divina: Luke 3:22; Psalm 29:3-4