Is the prayer valid for someone who remembered the prostration of forgetfulness (sujūd al-sahw) before the salām, after the first taslīm, then completed the second taslīm, and then performed the prostration of forgetfulness?

Your prayer is valid and you do not need to repeat it. What occurred does not affect its validity. The prostration of forgetfulness (sujud al-sahw) is valid both before and after the salutation. The post-salutation prostration (sujud al-ba'di) is valid if performed before the salutation, or the pre-salutation prostration (sujud al-qabli) if performed after it, whether done intentionally or unintentionally. If one forgets the prostration of forgetfulness and then remembers it before a long time has passed, they should perform it.