[Bug][DateInputPropsContext] The value of the DateInput is not set when a format value is passed through DateInputPropsContext

[Yanko-Georgiev]

Description

When the format property is set through DateInputPropsContext, the DatePicker does not update the value of the DateInput upon selection.

Plan

KendoReact Free

Steps To Reproduce

1. Open the following example: https://stackblitz.com/edit/react-jd17nhz4-bv9huj3g?file=app%2Fapp.tsx
2. Select a date
3. Notice that the value of the DateInput is not set

Actual Behavior

The value of the DateInput is not updated after a selection with the Calendar in a DatePicker.

Expected Behavior

Selecting a value from the Calendar in a DatePicker should update the value of the DateInput part.

Reported in TicketID: 1692082