Ubuntu Software in Ubuntu 20.04 is actually Snap Store. At the moment, you can not search for and install any application other than Snap packages via the utility.
A workaround is to install back the old Gnome Software, which is the default in previous Ubuntu releases and has exactly same user interface.
1. Open terminal either by pressing Ctrl+Alt+T on keyboard or by searching for ‘terminal’ from application menu.
2. When terminal opens, run command to install Gnome Software:
sudo apt install gnome-software
3. Once installed, refresh system package cache either via Software Updater or by running command:
sudo apt update
4. Finally launch Gnome Software from application menu and enjoy!