I’ll refrain from entering the discussion of whether or not NYC public school entry tests are culturally biased, but you can without a doubt prep for them if the kid is willing to do so.
Can’t speak to the boarding schools but at my school, the routine feeling was college - especially the first year or two, was easier than high school. In 8th grade I had a science teacher who had a checklist of formatting items he required on every lab report (things like properly labeled axes, tables with headers, etc) and if you missed any item on the checklist you got a 0 on the report no matter the quality of the rest of it. Actually a very important lesson for a future scientist with how competitive grant applications are.