Does the supplication: "O Lord, forgive everyone who has a right over me" suffice for the forgiveness of sins related to the rights of created beings, such as backbiting and cursing, and can one supplicate similarly for another person, such as one's mother or father?

If the sin relates to the rights of a human being and you know the person concerned, it is obligatory to seek their forgiveness unless there is a greater harm. If a greater harm exists, such as discord, some scholars are of the view that it is sufficient to seek Allah's forgiveness (istighfar) and supplicate for that person, along with sincere repentance. If the owners of the rights are unknown, then a general supplication for them may be a reason for Allah to lighten your burden and compensate the rightful owners. This supplication is permissible and good, and there is nothing to prevent Allah from responding to it.