Internal issue 3063 - Date Picker - Timezone change causes inconsistent UI

- Go to [Date picker - Intelligence Community Design System|https://design.sis.gov.uk/components/date-picker/code#icchange-event]) (IcChange Event demo)
- Click through the UI to select a date
- Keeping the window open, change your timezone westwards (like would happen when daylight savings ends)
- Re-open the date picker UI, and the day before the date you selected will be shown, and all the date numbers will have been shifted forward by 1, without shifting the day labels

See attached screenshot. with Wed 10 June 2025 showing as selected but 11/06/2025 in the text box. Also, 10 June 2025 was a Tuesday.

Start with the Date picker - Intelligence Community Design System demo linked in the issue and reproduce the behavior by selecting a date, then changing the timezone westwards while the window remains open. Trace the date-picker entry point responsible for reopening and rendering the selected date; done means the selected day, day labels, and text-box value remain consistent after the timezone change.

Written by the indexing model from the issue text.