Research on *non-top-layer* non-modal dialogs

I'm opening this issue to attempt to convince someone to do a bit of research. The context is provided by https://github.com/whatwg/html/issues/9376 and https://github.com/whatwg/html/issues/4633, but the TL/DR is:

We now have two ways to make a "non-modal dialog" in the platform:

1. <dialog id=foo> <script>foo.show()</script>
2. <dialog popover id=foo> <button popovertarget=foo>Click me</button>

Both of these have role=dialog as they should, but the issue at hand is that only #2 has the dialog in the top layer. The non-modal dialog in example #1 paints in its normal z-index position and can be obscured by other content.

So the question is: how common are non-top-layer dialogs? I.e. a dialog that allows interaction with the rest of the application/content, but which can be obscured and "go behind" some or all of the page content. This question can, and should, be answered for both web content and native content.

Is anyone interesting in kicking off this research? In my opinion, the best answer would consist of a list of example use cases for non-modal dialogs, a link to the specific implementation being researched, and a Y/N answer for whether that implementation has the dialog painted always-on-top.

Start with the context in WHATWG issues 9376 and 4633, then compare the two dialog examples in this issue with web and native implementations. Done means a list of non-modal dialog use cases, a link to each specific implementation, and a Y/N answer for whether each dialog is painted always-on-top.