For what it's worth, the Popover documentation is very explicit that <dialog> is the only right tool for the job when you want a modal:
modal, meaning that while a popover is being shown, the rest of the page is rendered non-interactive until the popover is actioned in some way (for example an important choice is made).
non-modal, meaning that the rest of the page can be interacted with while the popover is being shown.
Popovers created using the Popover API are always non-modal. If you want to create a modal popover, a
<dialog>element is the right way to go.