Half moves without capture or pawn move

How many of these are allowed prior to a draw being declared? 50?

That is the 50 MOVE rule, or 100 ply (half-moves)

I don't know whether it's already official or not, but I seem to
remember having read quite some time ago (might have been
ChessBase Magazine) that, since computer programmes win
endgames that were considered draws, the 50-move rule should be
extended to 100. Might also just have been suggesting the idea.
Humans can't, I suppose...

You are correct. FIDE tournaments are handling it on a case by case
basis. There are endgames that are now known to be winnable but
may require concession where the 50 move rule is concerned. Basically
if a player can demonstrate a winning technique, the rule is not
applied. For example, the Rook vs Bishop engame was until several
years ago, thought to be quite drawn, but computer analysis has
revealed a win by force. Though some lines require over 100 moves to
convert.