Try to install it in terminal this way:
sudo dnf install gnome-shell-extension-dash-to-dock
The extension manager from flatpak you get like (blue icon):
sudo flatpak install com.mattjakeman.ExtensionManager
The extension manager to browse extentions.gnome.org (green icon) you get:
sudo dnf install gnome-extensions-app
To get more than just the Fedora apps, you have to check “Software” > “Software Repositories”
if dl.flathub.org is active. Also to the “testing” flatpak repository can be switched on there if necessary.
