The court may grant a motion to open or set aside a judgment terminating parental rights pursuant to § 52-212 or 52-212a or pursuant to common law or may grant a petition for a new trial on the issue of the termination of parental rights, provided the court shall consider the best interest of the child, except that no such motion or petition may be granted if a final decree of adoption has been issued prior to the filing of any such motion or petition. Any person who has legal custody of the child or who has physical custody of the child pursuant to an agreement, including an agreement with the Department of Children and Families or a licensed child-placing agency, may provide evidence to the court concerning the best interest of the child at any hearing held on the motion to reopen or set aside a judgment terminating parental rights. For the purpose of this section, “best interest of the child” shall include, but not be limited to, a consideration of the age of the child, the nature of the relationship of the child with the caretaker of the child, the length of time the child has been in the custody of the caretaker, the nature of the relationship of the child with the birth parent, the length of time the child has been in the custody of the birth parent, any relationship that may exist between the child and siblings or other children in the caretaker’s household, and the psychological and medical needs of the child. The determination of the best interest of the child shall not be based on a consideration of the socio-economic status of the birth parent or the caretaker.