The handrail and brackets you reference will require a through BOLT not a self- tapping screw.
Because it’s 4’ long and stands off the face about 2” (1 1/2” is minimum by Code), the load on each end of handrail will be 300 lbs. / 2 = 150 lbs. at each connection. A 1/4” stainless steel through bolt would suffice for that. (1/4” bolt in double shear will hold 1 - 2 kips, depending on the grade of steel, etc.)
However, more importantly, because the bracket holds the handrail off the face of the post and the bracket does not have much of a resisting “arm” on the bottom of the bracket, the resistance is dependent on the size of the nut/washer, size of hole in post, etc.
If you look at their installation guide, they provide 2 - 5/16” lag wood screws. I doubt you’ll be able to modify the hole size to accept a larger bolt, so using a 5/16” stainless steel through bolt is probably your only option. The “weak link” to your system is going to be the thickness of the wall of your posts (which can be improved by using a larger washing on each side of the post).
Also, if you look closely at the installation instructions for the post, you’ll see it is designed to be screwed down to a wood deck. This will not work for your installation. You’ll need to modify the base and get expansion anchors to secure it to your slab.