`animate` glitches when `month` is controlled and the parent rerenders during navigation

## Summary

When `DayPicker` is used with `animate` and a controlled `month` prop, the month transition can glitch if the parent rerenders during `onMonthChange`.

This is easy to reproduce in the Docusaurus playground when `month` is synced to external state / query-string state, but it looks like a library-level robustness issue rather than a docs-only issue.

## Reproduction

```tsx
function ControlledAnimatedCalendar() {
const [month, setMonth] = useState(new Date(2026, 3, 1));
const [tick, setTick] = useState(0);

return (
{
setMonth(nextMonth);
setTick((x) => x + 1); // simulate external rerender / router update
}}
/>
);
}
```

## Actual behavior

The transition can briefly flicker, jump, overlap, or appear to reset mid-flight.

https://github.com/user-attachments/assets/9514497c-c1c0-4dc8-b33b-3979131dc2ee

## Expected behavior

Animated month transitions should remain stable when `month` is controlled, even if the parent rerenders during `onMonthChange`.

https://github.com/user-attachments/assets/6fce5b66-c73e-41dd-af69-ba641e35d79a

## Notes

- The Docusaurus playground makes this easy to trigger because it syncs props to the URL.
- A plain Vite example where month navigation stays internal to `DayPicker` does not show the same glitch.
- This suggests the issue is related to controlled animated navigation under extra rerender pressure.

## Suspected cause

`src/useAnimation.ts` appears to update animation snapshots/refs on every render. In controlled mode, parent rerenders during an ongoing transition may cause the animation bookkeeping to be refreshed from an already animating tree, which can desync the transition state from the DOM.

## Possible fixes

1. Only set up animation state when the displayed month actually changes, not on every rerender.
2. Keep one stable snapshot per transition and avoid overwriting it while an animation is active.
3. Add a regression test for `animate` + controlled `month` + parent rerender in `onMonthChange`.