Can I use wall rail brackets with heavy handrail?
Instead of wall bracket, I would use Rosette and, it looks great with hand-rail, also easy to attach as part of DYI.
I have handrail in my house and has this oak finished round Rosette attached to hand rail. The only different is my hand-rail in finished one. Buy any of the wood rosette whichever you like and meets your style.

Employee at Lowes can assist you what accessories you will need along with rosette.
Edited the answer after more clear. Here on wall side pic,

Hope this help!!