In order to install tailscale, on Fedora CoreOS (this post has been tested on Fedora CoreOS 35), you can use this sequence of commands:
sudo curl -o /etc/yum.repos.d/tailscale.repo https://pkgs.tailscale.com/stable/fedora/tailscale.repo sudo rpm-ostree install tailscale
Now reboot using
sudo systemctl reboot
Once rebooted, you can enable the service using
sudo systemctl enable --now tailscaled
and then configure tailscale as usual:
sudo tailscale up --login-server .... --authkey ...
Also see our post on How to connect tailscale to headscale server on Linux