Preloading maptiles for camera animation stopped working

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**mapbox-gl-js version**: 3.9.3, also confirmed in 3.6

**browser**: Chrome & Firefox confirmed

### Steps to Trigger Behavior

1. Add a mapboxgljs map
2. Preload maptiles and await idle before running flyTo.
Code example:
```js
map.flyTo({center: [-119.5375, 37.7425], preloadOnly: true});
await map.once('idle');
map.flyTo({center: [-119.5375, 37.7425]});
```

### Expected Behavior
Maptiles should be preloaded before animation starts for a smooth animation.

### Actual Behavior
Animation runs instantly, tiles are not preloaded. Resulting in a laggy animation.
The lag is more visible on a less performant device, such as a mobile phone.

Start with the provided mapbox-gl-js reproduction using flyTo({preloadOnly: true}) and the idle event, then compare it with the following animated flyTo call in Chrome and Firefox. Confirm that tiles are loaded before animation begins and that the animation is no longer instantaneous.

Written by the indexing model from the issue text.