fix(ui): recentre the board on a hint taken while already zoomed in

The board only scrolled to the hint's word when the hint also toggled zoom (the
zoom-out case): the recenter effect tracked `zoomed` and read `focus` untracked,
so a hint taken while ALREADY zoomed in — no zoom change — never recentred and
the board stayed parked where the player was looking.

Add a `recenter` nonce the hint bumps; the board's scroll effect tracks it and,
when it fires without a zoom toggle, pans straight to `focus` (the board width is
stable, so the width-driven zoom tween has nothing to ride). Placing a 2nd+ tile
or hovering a dragged tile still set `focus` without the nonce, so the board
never jumps on those — the original no-jump intent is preserved.

e2e: zoom into the corner, then hint (the mock plays at the centre) — the board
pans toward the centre. Verified RED without the fix (both engines), GREEN with.

ui/src/game/Board.svelte

@@ -20,6 +20,7 @@
     lines,
     locale,
     focus,
+    recenter,
     dropTarget,
     oncell,
     ontogglezoom,
@@ -39,6 +40,9 @@
     lines: boolean;
     locale: Locale;
     focus: { row: number; col: number } | null;
+    /** A monotonic nonce the parent bumps to request a scroll to `focus` even when the zoom state
+     *  is unchanged — the hint recentring an already-zoomed board on the word it played. */
+    recenter: number;
     /** The cell a dragged tile is currently aimed at, highlighted as a drop target. */
     dropTarget: { row: number; col: number } | null;
     oncell: (row: number, col: number) => void;
@@ -60,10 +64,17 @@
   // the board's real width grows (zoom-in) or shrinks (zoom-out), so it magnifies evenly
   // from A to B in one motion instead of chasing a per-frame target that the scroll bounds
   // clamp — which made the board lurch one way and then snap back near the edges/centre.
-  // It runs only on a zoom toggle (`zoomed`); changing `focus` while already zoomed does
-  // not recentre, so placing a 2nd+ tile or hovering a dragged tile never jumps the board.
+  // It tracks the zoom toggle (`zoomed`) and the `recenter` nonce; `focus` stays untracked,
+  // so placing a 2nd+ tile or hovering a dragged tile never jumps the board — only a zoom
+  // toggle or an explicit recenter request (the hint) moves it. A recenter with no zoom change
+  // pans straight to `focus`, since the board width is stable and the width-driven tween below
+  // has nothing to ride (the case the owner hit: a hint taken while already zoomed in).
+  // The previous zoom state, to tell a zoom toggle from a recenter request. The board always mounts
+  // zoomed-out, so it starts false and is updated to the live zoom on each effect run.
+  let prevZoom = false;
   $effect(() => {
     const on = zoomed;
+    void recenter; // re-run on an explicit recenter request even when the zoom state is unchanged
     const vp = viewport;
     if (!vp) return;
     const f = untrack(() => focus);
@@ -72,8 +83,6 @@
     if (clientW === 0) return;
     const fitW = clientW; // board width at scale 1 (fills the viewport)
     const fullW = clientW * Z; // board width at full zoom
-    const startSL = vp.scrollLeft;
-    const startST = vp.scrollTop;
     let finalSL = 0;
     let finalST = 0;
     if (on && f) {
@@ -81,6 +90,19 @@
       finalSL = Math.max(0, Math.min((f.col + 0.5) * cell - clientW / 2, fullW - clientW));
       finalST = Math.max(0, Math.min((f.row + 0.5) * cell - clientH / 2, fullW - clientH));
     }
+    const toggled = on !== prevZoom;
+    prevZoom = on;
+    if (!toggled) {
+      // No zoom change: an explicit recenter (the hint) pans straight to the focused word; a stale
+      // run with nothing focused leaves the scroll alone.
+      if (on && f) {
+        vp.scrollLeft = finalSL;
+        vp.scrollTop = finalST;
+      }
+      return;
+    }
+    const startSL = vp.scrollLeft;
+    const startST = vp.scrollTop;
     const fromW = on ? fitW : fullW; // board width when this transition begins
     const toW = on ? fullW : fitW;
     let raf = requestAnimationFrame(function tick() {

ui/src/game/Game.svelte

@@ -47,6 +47,10 @@
   let zoomed = $state(false);
   let selected = $state<number | null>(null);
   let focus = $state<{ row: number; col: number } | null>(null);
+  // Bumped to ask the board to scroll to `focus` even when the zoom state does not change — the
+  // hint recentring an already-zoomed board on the word it just played (a plain focus change is
+  // deliberately ignored by the board so placing/dragging tiles never jumps it).
+  let recenter = $state(0);
   // A stable id per rack slot, permuted together with the letters on shuffle, so the rack
   // tiles fly to their new positions (Rack's hop animation) instead of relabelling in place.
   let rackIds = $state<number[]>([]);
@@ -629,6 +633,10 @@
             row: Math.round((Math.min(...rows) + Math.max(...rows)) / 2),
             col: Math.round((Math.min(...cols) + Math.max(...cols)) / 2),
           };
+          // Ask the board to scroll to the hint word. A zoom-out board zooms in (and centres) on
+          // the next line; this nonce also recentres a board that is already zoomed in, where the
+          // unchanged zoom state would otherwise leave it parked where the player was looking.
+          recenter++;
         }
         if (isCoarse()) zoomed = true;
         view = { ...view, hintsRemaining: h.hintsRemaining };
@@ -929,6 +937,7 @@
           lines={app.boardLines}
           locale={app.locale}
           {focus}
+          {recenter}
           {dropTarget}
           oncell={onCell}
           ontogglezoom={(r, c) => { focus = { row: r, col: c }; if (!gameOver) zoomed = !zoomed; }}