I speak several languages too, though definitely not as many as you do. I'm also in the process of learning a completely new one, at an advanced age relative to when I last learned a new one (I was in my thirties then). To me, my brain most definitely doesn't process human language the way it handles computer language. It's about as different as it can get. The latter is "learning", the former is "burn patterns into the brain", and learning a language can take years, at least at this age. Computer languages? Those can be picked up in as little as a weekend, and getting proficient isn't a multi-year or decade long process. It feels totally different for me (I've been learning new computer languages at the same time as I've been trying to get up to speed with a new human language).
Computer languages are much simpler than human languages, and they also operate in similar kind of logical ways. I definitely remember how hard was to go from pascal to C to Cpp to Python to prolog to haskell to SQL... until at some point nothing was new.