Does the noble verse: (And provide you with wealth and children and make for you gardens and make for you rivers) mean that Allah will provide the unmarried woman with a husband and children, or is it specific to married men and women?

We have not come across anything that indicates the تخصيص (specific allocation) of the verse of seeking forgiveness (Ayat al-Istighfar) to married individuals. Rather, what is apparent is the generality of the promise for all those who seek forgiveness. Seeking forgiveness is one of the reasons for marriage and progeny. In His (Allah's) saying, "He will let you enjoy a good enjoyment" (Quran 11:3), marriage and children are included. Many stories have been narrated about the facilitation of marriage and childbirth through seeking forgiveness.