Does the thief remain sinful and the money he owes remain forbidden to him if he confesses his act, promises to repay, and commits to prayer and seeking forgiveness?

Theft is one of the major sins. If a person steals, he must repent to Allah and return the stolen item to its owner. If the owner of the property forgives him, then he is absolved. Therefore, if the thief repents with sincere repentance and returns the money or is forgiven by the owner of the money, then he no longer remains a sinner.