In Georgia (and the way my association does it) there is a paid PCM or Pitch Count Monitor and the coaches are told at the plate meeting to give a second copy of the lineup (a preseason meeting told them to list first and last names) and the HP umpire gives the PCM a copy of the lineup. After the game, the HP umpire gets the pitch count sheet and takes a picture which is sent to our assignor. There is a website the pitch count totals are entered on, and then a central database anyone can go to & pull up a particular school on a particular date in order to see pitch totals for the players.
The website the pitch count totals are on is maintained by the GHSA.
As a side note, coaches are told at the plate meeting they can inquire or ask about pitch totals in between 1/2 innings but they have to go through the HP umpire & can't speak directly to the PCM. And whatever totals the PCM has is the official total.