Does the emission of semen after eating at night, without desire, necessitate Ghusl, and is it obligatory to re-perform past prayers if one did not perform Ghusl?

You erred in applying the fatwa (definition) regarding the non-obligation of ghusl (definition) (ritual bath) for semen discharge without desire to your specific situation, as that ruling applies to someone who is awake. However, for a sleeping person, if they find semen after waking up, ghusl becomes obligatory, based on the hadith (definition) narrated by Aisha: "The Messenger of Allah (peace be upon him) was asked about a man who finds wetness but does not remember a wet dream. He said: 'He should perform ghusl.'" Therefore, you must repeat the prayers you performed after seeing semen without having performed ghusl. This opinion is more cautious.