Drop the slot add add a screencast-legacy plug to your app declaration, see https://snapcraft.io/docs/the-screencast-legacy-interface. You will need to connect the plug manually, eg. snap connect <yoursnap>:screencast-legacy system:screencast-legacy.
Note that neither the org.gnome.Shell.Screencast or org.freedesktop.portal.ScreenCast interfaces are going to work on Ubuntu releases prior to 21.04 (hirsute). They rely on gnome-shell (and xdg-desktop-portal for the portal interface) being built with Pipewire support, which wasn’t the case for Ubuntu 20.10 and earlier.
If you are running Hirsute, or some other system with a Pipewire enabled gnome-shell+xdg-desktop-portal, then you should be able to use the portal interface simply by plugging the desktop interface.
Sorry, I hadn’t double-checked 20.04. The interface is definitely missing in Ubuntu 20.10, likely because they replaced the old implementation with one depending on Pipewire.
The xdg-desktop-portal interface is a wrapper for gnome-shell’s org.gnome.Mutter.ScreenCast D-Bus interface, which definitely isn’t available in the older Ubuntu releases.