whos job is it to enforce the 1 match suspension for too many yellows does the club have to count them and then make the player sit out? or does the ghfa have to inform the club that the player has hit the limit?

GHFA sends a list to the clubs.

so if youre pretty sure youre on 4 yellows but your club hasnt heard anything from the ghfa youre good to play?

Yep, Very common for refs to not mark down cards. For yellow cards, your only suspended if your advised by the GHFA. For reds, its auto 1 match, then if it's more they will advise you.