I discussed the issue on the Red Hat Bugzilla (https://bugzilla.redhat.com/show_bug.cgi?id=2325904). As their answer explainexplains quite well the why and how, I reproduce it here.
Versions of docker-compose
Fedora 40 provides docker-compose v1.x and Fedora 41 provides docker-compose v2.x. With version 2, the docker-compose team switched to implementing the compose functionality as a plug-in to docker. In version 1 docker-compose is a stand-alone application. The docker-compose team now provides a separate component (see https://github.com/docker/compose-switch) to emulate the stand-alone client functionality. This functionality is now available in Fedora 41 (and newer) as docker-compose-switch.
Install from Docker rpms
If you are installing docker using rpms from the Docker community (e.g. docker-compose-plugin rpm), then the instructions provided at https://github.com/docker/compose-switch can be followed to regain docker-compose at the command line with the compose v2 functionality.
Install from Fedora rpms
To implement docker-compose from Fedora rpms, please remove the Docker rpms such as docker-ce-stable and docker-compose-plugin and then using 'sudo dnf install docker-compose-switch'. This will then include the docker-compose rpm (as a plugin) and suggest the containerd rpm which contains docker. Alternatively podman-docker can be installed to provide a docker alias which will also work with the plug-in.