[popover] Popover opened on mouse focus stays open if target click opens the dialog

[web-padawan]

Description

This is similar to #8197 but related to focus trigger (especially mouse focus) so I decided to create a separate issue.

Expected outcome

Expected the popover to not open on target focusin when there's already another overlay opened on target click:

popover-dialog.mp4

Note, opening the dialog doesn't move focus to it immediately so that focusin event is still handled by popover.

Minimal reproducible example

<vaadin-button id="button">Target</vaadin-button>

<vaadin-popover for="button" position="bottom-start"></vaadin-popover>

<vaadin-dialog></vaadin-dialog>

<script type="module">
  import '@vaadin/button';
  import '@vaadin/dialog';
  import '@vaadin/popover';

  const popover = document.querySelector('vaadin-popover');
  popover.trigger = ['focus'];

  const dialog = document.querySelector('vaadin-dialog');
  const button = document.querySelector('vaadin-button');

  button.addEventListener('click', () => {
    dialog.opened = true;
  });

  popover.renderer = (root) => {
    root.textContent = 'Popover text';
  };

  dialog.renderer = (root) => {
    root.textContent = 'Dialog content';
  }
</script>

Steps to reproduce

1. Click the button so that dialog opens
2. Popover will open soon after dialog and will be on top of it

Environment

Vaadin version(s): 24.5, 24.6

Browsers

Issue is not browser related