Honestly, i doubt that anyone will do the server part in R. The R community always glued other better suited languages for specific parts (fortran/c for optimization, js for frontends like shiny, c++ for computationally intensive task ...).
If you look closely at httr/httr2 it is a wrapper of curl (R package) which is a wrapper for the curl c library - so technically the big chunk of the network communication is done via c.