Does this dream mean that a specific action is obligatory, and what should I do to understand what is permissible for me to do, and is it permissible for me to supplicate to Allah to unite me with this person in Paradise?

Nothing is mandated by a vision. The prayer of an unrelated man and woman that Allah unite them in Paradise is impermissible for a married woman and is considered an transgression. As for an unmarried woman, it is originally permissible, and it is recommended to hasten to marriage, which may even become obligatory. If she gets married, there will be no room for such a prayer.