Is it obligatory to make up the prayers missed years ago due to delaying the post-menstrual bath, given that their number is unknown?

What you did, delaying the ritual bath (ghusl (definition)) after menstruation, is a major mistake and a grave sin. You must hasten to repent. You are required to make up the prayers missed over the past years. If you cannot determine their exact number, then you should continue making them up until you are reasonably certain that your obligation has been fulfilled. Sheikh al-Islam Ibn Taymiyyah held the view that making up prayers is not obligatory for someone excused by ignorance, citing the hadith (definition) of the woman with prolonged bleeding (Mustahadah) and how the Prophet, peace and blessings be upon him, did not command her to make up past prayers. He also noted the presence of many people in rural and urban areas who reach puberty but do not know that prayer is obligatory.