How to mount handrail brackets to a concrete block wall

I solved the same problem by with t-nuts. Embed the t-nuts into the stud, or in my case a wooden brace between the studs. Then attach the bracket to the t-nut with a machine bolt. I've screwed and unscrewed the bolt repeatedly but because it is metal-to-metal it does not compromise the wood and thus does not wobble.

(I agree this question is different than the one about a removable stair railing because this railing goes into the wall).

I haven't yet figured out how to mount such a wall rail into masonry. A 2-part or removable bracket, as you ask, seems like a good idea but I haven't found one yet.

Yes, you should add rebar across the joint between to old and new block wall. Do this by using a masonry drill (preferably a hammer drill) and drill 3-6" vertically down into the existing block wall top where the hole / rebar dowel will not be in the way of adding the next row of block. Best to use 1/2" or #4 rebar for this purpose and use the same size masonry drill bit to do your drilling. It's best to get the block cut and placed into position before you do the drilling to be sure there's no placement conflict between the intended new block layer and the rebar dowel holes to be drilled. Once you have them laid out on the wall then you can mark the hole's placement. I'd use a dowel in each corner hole and at least every other hole in the new block's run. Cut your rebar dowel length the depth of the drilled hole plus the block layer height minus 1-2" so they don't stick out of the new walls top. Fully insert the dowel into the drilled hole by hammering the rebar into the hole with a 2-3# mallet until they hit then end of the drilled hole.

*Rebar is meant to provide stability for the rigid concrete matrix or material. The reason you see rebar in bridges is that while the concrete provides a platform to drive on it's very rigid and will break apart if stressed past it's physical abilities. The rebar in the bridge keeps the concrete or matrix or material together and aligned in case of cracks in the concrete and strengthens the overall concrete structure with much less steel than in a conventional steel only bridge structure.