user15543: 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.)

user21604: I interpret the following

White will play as long as possible, and not want to lose. Black will claim a draw as soon as possible, if not win

as meaning that Black does not help (i.e., Black tries to either win or draw as fast as possible, while White tries to make the game as long as possible and then draw or win). I suggest the following position with 1865 moves.
[FEN "7k/8/4N3/6N1/8/8/PPPPPPPP/4K3 w - - 0 1"]

It seems to me that White can do 6 moves with each of the 4 left-side pawns (each one promotes to a bishop on its last move), then (3, 4, 2, 4) moves with the remaining four pawns. Before the first pawn move, White can play 13 waiting moves with the king while avoiding threefold repetition. Between each subsequent pawn move, White can play 49 waiting moves with their king. This gives 13 + 36 x 50 = 1813 moves. As moves 1814 and 1815, White does the following
[FEN "BBBB2k1/8/4NP1P/4P1N1/6P1/8/8/4K3 w - - 0 1"]

1. f7+ Kh8 2. f8=N Kg8

and then White makes 50 more waiting moves before drawing at move 1865.

user4418: The answer is trivially the starting position -
[fen ""]

This exact question hasn't been asked before (I think) but it has been answered here. Here is the relevant part of that answer -

The maximum number of moves in a chess game is not infinite, it's
11797 plies = 5898 moves and a half. This is due to the fifty-move
rule.

As an interim possibility here is an obvious extension of the OP's original position (before he made dozens of edits):
[FEN "5b1k/p1p1p1p1/P1P1P1P1/8/8/8/P1P1P2P/RNBQKBNR w - - 0 1"]

White makes the same starting pawn and king moves as in the OP's post minus allowing any captures and then brings a piece out to capture the a pawn, taking 49 moves to do that, then queens one of the a pawns taking 49 moves per pawn move, then takes 49 moves to sacrifice that queen next to the king, then same again with white's other a pawn, ditto taking the c pawn, etc., etc.

15543: <p>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.</p>
<p>Here is my starting offer of <strong>703 moves</strong></p>
<pre><code>[FEN &quot;5bkq/p1p1p1pR/P1P1P1P1/8/4K3/8/P1P1P2P/7n w - - 0 1&quot;]

1. Rxh8+ Kxh8 2. Kf3 Nf2 3. Kxf2
</code></pre>
<p>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.)</p>
 21604: <p>I interpret the following</p>
<blockquote>
<p>White will play as long as possible, and not want to lose. Black will claim a draw as soon as possible, if not win</p>
</blockquote>
<p>as meaning that <strong>Black does not help</strong> (i.e., Black tries to either win or draw as fast as possible, while White tries to make the game as long as possible and then draw or win). I suggest the following position with <strong>1865 moves</strong>.</p>
<pre><code>[FEN &quot;7k/8/4N3/6N1/8/8/PPPPPPPP/4K3 w - - 0 1&quot;]
</code></pre>
<p>It seems to me that White can do 6 moves with each of the 4 left-side pawns (each one promotes to a bishop on its last move), then (3, 4, 2, 4) moves with the remaining four pawns. Before the first pawn move, White can play 13 waiting moves with the king while avoiding threefold repetition. Between each subsequent pawn move, White can play 49 waiting moves with their king. This gives 13 + 36 x 50 = 1813 moves. As moves 1814 and 1815, White does the following</p>
<pre><code>[FEN &quot;BBBB2k1/8/4NP1P/4P1N1/6P1/8/8/4K3 w - - 0 1&quot;]

1. f7+ Kh8 2. f8=N Kg8
</code></pre>
<p>and then White makes 50 more waiting moves before drawing at move <strong>1865</strong>.</p>
 4418: <p>The answer is trivially the starting position -</p>
<pre><code>[fen &quot;&quot;]
</code></pre>
<p>This exact question hasn't been asked before (I think) but it has been answered <a href="https://chess.stackexchange.com/questions/8331/is-the-number-of-possible-chess-games-infinite/8334#8334">here</a>. Here is the relevant part of that answer -</p>
<blockquote>
<p>The maximum number of moves in a chess game is not infinite, it's
11797 plies = 5898 moves and a half. This is due to the fifty-move
rule.</p>
</blockquote>
<p>As an interim possibility here is an obvious extension of the OP's original position (before he made dozens of edits):</p>
<pre><code>[FEN &quot;5b1k/p1p1p1p1/P1P1P1P1/8/8/8/P1P1P2P/RNBQKBNR w - - 0 1&quot;]
</code></pre>
<p>White makes the same starting pawn and king moves as in the OP's post minus allowing any captures and then brings a piece out to capture the a pawn, taking 49 moves to do that, then queens one of the a pawns taking 49 moves per pawn move, then takes 49 moves to sacrifice that queen next to the king, then same again with white's other a pawn, ditto taking the c pawn, etc., etc.</p>
