text-input.applyOnBlur issues in picker

[nclemeur]

Describe the bug
When using `:text-input="{applyOnBlur: true}", it seems that the time picker arrows are not working if the first click in the date picker menu is on one of the arrows that control the time.

To Reproduce
Steps to reproduce the behavior:

1. Go to this stackblitz
2. Click on the input text to open the date picker (notice that the date is selected in the calendar and is shown correctly in the preview, see screenshot 1)
3. Click on the any arrow of the time picker
4. The time preview is gone and the date is not selected anymore (see screenshot 2)

Expected behavior
I would not expect the date to be unselected in the picker and the time preview cleared. I actually just noticed now that it's not limited to the time picker arrow, but if you click anywhere in the picker that is not a date, you obtain the same issue...

Screenshots
Screenshot 1:

Screenshot 2:

Desktop & mobile (please complete the following information):

• Browser chrome

[beanscg]

I looked at the current input component, and the repro matches the blur ordering in DatepickerInput.vue.

The key branch is in handleBlur():

if (
  (rootProps.autoApply && textInput.value.enabled && parsedDate.value && !props.isMenuOpen) ||
  textInput.value.applyOnBlur
) {
  emit('set-input-date', parsedDate.value);
  emit('select-date');
  parsedDate.value = null;
}

The autoApply side is guarded by !props.isMenuOpen, but the applyOnBlur side is not. So with applyOnBlur: true, the first click inside the picker can blur the text input while the menu is still open, emit set-input-date/select-date, and clear parsedDate before the time-arrow click finishes.

The regression I would add is:

• open the menu with text-input.applyOnBlur: true,
• click a non-date control inside the menu, especially a time arrow,
• assert the selected date/preview is not cleared and the time control still applies.

A likely fix direction is to apply the same "menu is open" guard to the applyOnBlur branch, or otherwise distinguish a real outside blur from focus moving into the picker.