Replace wrought iron railing
Brackets of any kind will be inherently weak, if all you do is butt the 4x4 post to the top of the landing. It'll never be solid.
Your best bet is to cut a deep rabbet in the post so half of its 3-1/2" width extends down the side of the precast unit. That way you're attaching the rail to the side, which will be much stronger. Half the post's width sits on top of the landing or the tread of the stair, and the vertical "notch" or rabbet is used to secure it to the side of the monolith.
As far as bolts go, there are a few options. It depends how far you can get from the edges. You don't want to drill an expanding anchor 1" from the top of a stair tread or the top of the landing. You want at least a couple inches of concrete if you use a wedge anchor, which would work fine.
If it were mine, I'd drill holes and insert 1/2" galvanized threaded rod into the concrete using concrete epoxy. Very strong way of doing it, without risking cracking the precast stairs. Drill holes in the post and mark the locations on the concrete, then drill the concrete. Once the epoxy is set, you simply slip the post onto the pieces of all-thread and use nuts and washers to draw it down tight.
Other options include tapcons, lag screws with lead shields, etc.