GNOME Shell extensions are JavaScript monkey patch injections to gnome-shell's JavaScript process. They're only compatible with the exact version of gnome-shell that they target because most of them require to override private internals of gnome-shell that are sensitive to order of injection and names of private variables and methods.
COSMIC uses a modern Wayland-based approach to shell interface design with layer-shell applets. Each applet is its own process, using the layer-shell Wayland protocol to render their windows as shell components, and communicating with the compositor securely with the security context Wayland protocol. The protocols they use are standardized, so they will be stable across COSMIC releases. Other Wayland compositors could integrate with them if they desire to.