If you would like to install docker-compose on silverblue, you need to layer two packages, moby-engine and docker-compose.
You can do it with this command:
rpm-ostree install moby-engine docker-compose and do a reboot
Moby engine will provide a docker engine, because docker is not installed by default on Fedora Silverblue and docker-compose needa it. But there is a problem because Fedora runs on Cgroups V2 from version 30, and moby-engine in fedora repo currently does not support it so will not work. You can wait untill moby-engine in fesora repo will be upgraded to 20.10 version that supports Cgroups V2 or switch your system to legacy Cgroups V1 (this can break podman containers and toolboxes).
There is an alternative tool
podman-compose that will work out of box and is compatible with standard docker-compose files, you can layer it by typing:
rpm-ostree install podman-compose and reboot. It will just start working after reboot.