Gnome 49 and systemd
Gnome 49 switched from the builtin service manager to a systemd session startup.
For this reason all the desktop-related services adapted their behaviour to work with systemd.
Gnome Software switched too, and its .desktop file was replaced by a user service managed by systemd.
Preventing Gnome Software service autostart
The systemctl’s mask command can prevent a service from being started.
Mask one or more units, as specified on the command line. This will link these unit files to /dev/null, making it impossible to start them. This is a stronger version of disable, since it prohibits all kinds of activation of the unit, including enablement and manual activation. Use this option with care.
It can be used to block Gnome Software user service.
systemctl --user mask gnome-software.service
Because Gnome Software will no longer start automatically at login, no notifications about updates will be display. For the same reason, no updates will be automatically downloaded.
Disable Gnome Software search provider
Open the Settings application, go to the Search panel and disable the Gnome Software item in the Search Results list.
Enable Gnome Software to run as an application
To continue using the Gnome Software application a custom .desktop file must be created.
cp /usr/share/applications/org.gnome.Software.desktop ~/.local/share/applications/
But it needs to be updated in order to block it from starting on its own.
Edit your ~/.local/share/applications/org.gnome.Software.desktop file and set the DBusActivable option to false.
DBusActivatable=false
Removing Gnome Software and Alternatives
If Gnome Software is not needed at all, it can be removed with just one command.
sudo dnf remove gnome-software
An alternative GUI application (only for installing flatpacks) is Bazaar.
References
Original solution source: Fedora discussion.