How can one stop masturbating, a habit that has been with me for over 10 years, especially after it has caused me psychological distress and failure in my engagement, knowing that I fear dying while committing this sin?

You must repent to Allah Almighty with sincere repentance, accompanied by remorse and a firm resolve not to return to the sin. Be wary of persisting in disobedience. The remedy is marriage; if that is not possible, then fasting, along with increasing acts of obedience, staying away from sexual provocations, occupying oneself with what is beneficial, accompanying righteous company, and avoiding seclusion. This is because such practices have physical and psychological harms.