Is a person considered sinful if they change their statements under oath in court to reduce the punishment of a thief, after reconciliation and the recovery of the stolen goods, with the intention of lightening the sentence for him and to prevent his wife from leaving their home?

It would have been more appropriate for you, if you intended to relieve the person and help them, to do so without lying. You could have used dissimulation (tawriyah) and allusion (ta'rid) to avoid lying. If you have lied, then you must repent to Allah and seek His forgiveness, and do not return to that.