Add integration for Gnome extension "AATWS - Advanced Alt-Tab Window Swiitcher"

# Describe the feature you'd like
I love TilingShell's "Add tiled windows to ALT+TAB men" feature, however, I use the [AATWS Gnome extension](https://extensions.gnome.org/extension/4412/advanced-alttab-window-switcher/) ([GitHub reposiitory](https://github.com/G-dH/advanced-alttab-window-switcher)), which overrides Gnome's default alt+tab menu.

Understandably, the two don't automagically work together, and tiled windows don't show up in the AATWS menu. For me personally, the extra features of AATWS are worth the sacrifice of TilingShell's window groups showing up in the alt+tab menu, so I continue to use that extension, but I would love to have my beautiful tiled windows back in the alt+tab menu.

I imagine that any such integration will be hacky without the coordination of the two projects, since from my cursory glance over the projects, both projects override some or all of the built in switcher. So, I know it's not a simple ask : )

# Additional context
A [corresponding feature request](https://github.com/G-dH/advanced-alttab-window-switcher/issues/167) exists on their end, for whatever that's worth. The discussion seems to have fizzled out, however.

**Thanks!**

Start by reading this issue and the linked AATWS repository and feature request #167 to understand how both extensions replace GNOME's Alt-Tab switcher. Done means tiled windows and TilingShell window groups appear correctly in the AATWS menu without breaking either extension.

Written by the indexing model from the issue text.