The verb belongs to God. You will keep. The peace is not manufactured by the person having it.
That matters, because most peace advice is a set of instructions. Breathe, reframe, stop catastrophising. Some of it helps. None of it is what this verse describes.
Here the steadfast mind is not the cause of the peace. It is the posture that receives it. The mind is steady because it is fixed on something, and the something is doing the keeping.
Which explains why peace collapses when your attention moves. Nothing has changed about God in the hour you spent scrolling the worst possible outcome. What changed is where the mind was pointed.
So the practical work is smaller than it looks. Not producing calm out of nothing. Returning attention, repeatedly and unglamorously, to the one who was going to keep you anyway. You will do that many times today. Each return counts.