Backends can implement a subset of the interfaces, and xdp can be configured to try multiple backends in sequence until it finds one that provides the interface that the application wants. Eg xdp-wlr for wlroots-based Wayland compositors only implements compositor-specific interfaces like screencast, so users would chain it with something like xdp-gtk for other interfaces like file picker.
Native applications usually use their toolkits' API for showing file picker dialogs etc, and xdp's file picker interface is primarily used by flatpak applications since that is a way for sandboxed applications to read/write outside their sandbox. But it's not impossible for native applications to also use it, as zed is doing.
https://flatpak.github.io/xdg-desktop-portal/docs/api-refere...
Unless I missed it, the video doesn't actually answer the question. They talk 38:50 onwards about how they don't want to pull in GTK / Qt as dependencies, rather they just want to be able to read the toolkits' config and render a mimicking UI themselves. Then they show the editor opening a "native" file dialog, but don't actually say how exactly they did it.
Anyway, I assumed they would use xdg-desktop-portal, and based on searching the repo that does seem to be the case.