Must one repeat the prayers—the supererogatory ones or only the obligatory ones—that were performed in a previous period when there was doubt about the ritual bath (ghusl) after masturbation? And is ignorance an excuse in this case?

If you are certain that you performed prayers while in a state of janabah (major ritual impurity) without purification, you are obligated to make up those obligatory prayers you performed after reaching puberty, based on the principle that the original state of impurity remains until its removal is established with certainty. If you doubt your state of purity after being certain of janabah, the original state is that the impurity remains. If you are unable to determine the number of prayers, then strive to estimate what you believe most likely discharges your responsibility, and make up what will not cause you undue hardship. It is permissible to adopt the view of those who do not obligate making up prayers for someone who omitted a condition out of ignorance, although the first opinion is more cautious.