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.
This assurance, in and of itself, is not the main issue. If your ground of assurance is not the grace of God in Christ, then your assurance is presumption. Your heart is not established with grace until you see yourself as dead to sin and dead to the law. As long as you see any possibility of condemnation based on your sins, or any hope of assurance, glory, or reward, based on your obedience, your heart is not established with grace. God's people persevere in believing that their final glory is certain based on the righteousness of Christ.