Going by rules strictly about the board state, how long can a player theoretically hold off a draw by the 50-move rule? White will play as long as possible, and not want to lose. Black will claim a draw as soon as possible, if not win, so threefold repetition and dead position apply.
Here is my starting offer of 703 moves
[FEN "5bkq/p1p1p1pR/P1P1P1P1/8/4K3/8/P1P1P2P/7n w - - 0 1"] 1. Rxh8+ Kxh8 2. Kf3 Nf2 3. Kxf2
After taking 1 move to capture the queen and 2 for the Black knight, White starts the 50-move reset counter. White shuffles around their king to avoid repetition while Black's king is entombed. Every 50 moves thereafter, White plays a pawn move, with 12 total (playing h6 loses). After the 12th one, it will be another 50 moves until Black may rest: 1+2+50+(12*50)+50=704. (White's h-pawn position prevents dead position.)