What should I do after I made a covenant with God, saying: "I vow to You, O Lord, that if I marry anyone other than her, I will die not upon my religion," and now I wish to marry another woman?

What you mentioned in your question about the oaths and reprehensible sayings, and in the Hadith: "Whoever swears by a religion other than Islam, lying, then he is as he said." It is obligatory for you to repent and seek forgiveness, and to resolve not to return to such sayings. The preponderant opinion is that it is an oath, and it is safer to offer an expiation for an oath, which is feeding ten poor people, or clothing them, or freeing a slave. If you cannot find any of these, then fasting for three days.