@akaster ...oh I think I understand what you mean. You mean the user being able to "tear off" the tab and have *the whole tab content (the webview) move into its own window* while being dragged, like Chrome used to do. I don't know much about the client/toolkit side of this, but as far as Wayland protocols go you're going to need xdg-toplevel-drag, see this blog post https://blog.david-redondo.de/kde/wayland/qt/2023/08/08/xdg-toplevel-drag.html
The Qt pull request is here https://codereview.qt-project.org/c/qt/qtwayland/+/470673, see if you can make sense of it & figure out how to use it as an app/widget developer.
macOS, I don't know if there's a non-hacky way to do this (the hacky way would be creating a new NSWindow at just the right coordinates once you detect your tab is being torn off, and messing with events to keep the newly created window dragged), but I wouldn't advise you to do that either: let the system widgetry do its thing.
GTK/libadwaita, too, that's a feature that AdwTabView/AdwTabBar should implement (or not), not an individual app. You might want to talk to Alice M. about hooking up xdg-toplevel-drag to AdwTabBar.