react-day-picker `timeZone` prop breaks Persian calendar rendering for old years (e.g. 1313) in `Asia/Tehran`

1. When using the timeZone prop with the Persian calendar, DayPicker fails to render correctly for old years (for example, year "1313" in the Asia/Tehran timezone). The calendar grid and month view disappear or display incorrectly.

[1] To reproduce

Go to https://daypicker.dev/playground
Set Caption Layout → Dropdown
Set Calendar → persian
Set Time Zone → Asia/Tehran
- (If Asia/Tehran is not available, set your operating system timezone to Asia/Tehran and refresh the page)
Select 1313 (or another old year) from the year selector
Alternatively, open this direct link: https://daypicker.dev/playground?captionLayout=dropdown&dir=rtl&calendar=persian&locale=fa-IR&timeZone=Asia/Tehran

Expected Behavior

The calendar should correctly display all months and days for the selected year, regardless of how old the year is.

Actual Behavior

For older years (e.g. 1313), the calendar UI breaks — months and days are not rendered properly.

Screenshots

2. It also behaves incorrectly during DST transitions. For example, for 1401-01-02, as shown in the screenshots, the second day is displayed as 1 instead of 2, which is incorrect. Additionally, it throws a React “duplicate key” error. This happens because the @date-fns/tz doesn't handle the DST transitions correctly. A potential solution would be to use Luxon, which provides more reliable time zone and DST handling

[2] To reproduce

Go to https://daypicker.dev/playground
Set Caption Layout → Dropdown
Set Calendar → persian
Set Time Zone → Asia/Tehran
- (If Asia/Tehran is not available, set your operating system timezone to Asia/Tehran and refresh the page)
Select 1401 from the year selector and select "فروردین" from the month selector.