Merge branch 'perf/lag': dashboard lag fixes

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

# Conflicts:
#	client/src/components/Sagi/PetSprite.tsx
#	client/src/components/Sagi/useSagiBrain.ts

client/src/components/Sagi/PetSprite.tsx

@@ -63,6 +63,8 @@ const ACTION_ROW: Record<PetAction, number> = { "run-right": 1, "run-left": 2, w
 /** A moment's row: wave, jump, failed, waiting, review. It outranks the mood,
  *  and the user's own action outranks it. */
 const MOMENT_ROW: Record<PetMoment, number> = { wave: 3, jump: 4, fail: 5, wait: 6, review: 8 };
+/** Loops of a row before the sprite rests on its first frame. */
+const SPRITE_LOOPS = 4;
 
 export function PetSprite({
   id,
@@ -102,13 +104,17 @@ export function PetSprite({
     const own = play(row, sleeping ? SLEEP_SLOWDOWN : 1);
     let list = MOMENTS.has(row) ? [...own, ...own, ...own] : own;
     let i = 0;
+    let loops = 0;
     let timer = 0;
-    // `i` always indexes `list`: it wraps at its end.
+    // `i` always indexes `list`: it wraps at its end. A few loops, then the
+    // first frame rests — a sprite that never stops re-paints the page several
+    // times a second for as long as it is open; a new mood or action plays again.
     const tick = () => {
       timer = window.setTimeout(() => {
         if (++i === list.length) {
           i = 0;
           if (MOMENTS.has(row)) list = play(0);
+          if (++loops >= SPRITE_LOOPS) return setCell(list[0]!);
         }
         setCell(list[i]!);
         tick();