[date-picker] The input element is not cleared when closing the dropdown after deselecting a date

[vursen]

Description

A finding from #5625

Closing the dropdown by clicking outside after deselecting a date through the dropdown results in the input element not getting cleared.

Screen.Recording.2023-03-08.at.13.08.28.mov

Expected outcome

The input element should be cleared after the date selection is removed and the dropdown is closed.

Minimal reproducible example

<script type="module">
  import '@vaadin/date-picker';
</script>

<vaadin-date-picker></vaadin-date-picker>

Steps to reproduce

1. Focus on the date-picker
2. Open the dropdown with ArrowDown
3. Select a date through the dropdown with Space
4. Deselect the date with Space
5. Click outside the date-picker

Result: The selected date is still displayed in the input element despite no value.

Environment

Vaadin version(s): 24 and possibly earlier
OS: Mac OS

Browsers

No response