[date-time-picker] Tooltip does not hide when opening time picker dropdown

[sissbruecker]

Description

For a date time picker with a tooltip, the tooltip does not hide when opening the time picker dropdown using keyboard navigation. This has the side effect that pressing escape will first close the tooltip, and only a second escape press closes the time picker dropdown.

Expected outcome

I would expect the tooltip to disappear when opening the time picker dropdown, as opening the date picker dropdown also hides the tooltip.

Minimal reproducible example

    <vaadin-date-time-picker
      label="Birth date and time"
      error-message="error-message"
      min="2019-09-01T08:00"
      max="2019-09-30T22:00"
    >
      <vaadin-tooltip slot="tooltip" text="You will have a personal discount"></vaadin-tooltip>
    </vaadin-date-time-picker>

Steps to reproduce

1. Add the snippet to a page
2. Press Tab twice to focus time picker
3. Tooltip should be visible
4. Press down arrow key to open time picker
5. Tooltip is still visible behind dropdown

Environment

Vaadin version(s): 23.2

Browsers

Issue is not browser related