Irresistible grace shows us that God the Holy Spirit brings God's elect into salvation by convincing them of sin, of righteousness, and of judgment. It shows that by nature we all hate the light of the Gospel that shows us how we are lost and our deeds are evil. We are commanded to seek and believe that light and to reject all else in salvation. This is the general call of the Gospel. It is not because they do not have the faculties of mind and reason and will.
People can choose what they want.
But by nature we do not want salvation God's way, so as to glorify Him, exalt Christ, and exclude boasting in ourselves. By nature we want it our way. Perseverance of the saints shows us that we are kept by the power of God based on the righteousness of Christ, and all who are convinced of God's Gospel will continue in the faith seeing themselves as certain for heaven based on the merits of Christ. The established heart has to do with a person who is assured of salvation. Many people have assurance of salvation to one degree or another.