Maybe the software is already installed after running the AppImage? Try searching for the software in the applications overview and start it from there, or try running electrum
in a terminal.
If the above didn't worked then the AppImage they have provided is for testing the software, not downloading it. You can download the software by the following commands:
If you want snap
(The snap version of the app is out of date and may break):
sudo snap install electrum
If you want to manually compile:
sudo apt-get update
sudo apt-get install python3-pyqt5 libsecp256k1-0 python3-cryptography
wget https://download.electrum.org/4.1.5/Electrum-4.1.5.tar.gz
wget https://download.electrum.org/4.1.5/Electrum-4.1.5.tar.gz.ThomasV.asc
gpg --verify Electrum-4.1.5.tar.gz.ThomasV.asc Electrum-4.1.5.tar.gz
wget https://download.electrum.org/4.1.5/Electrum-4.1.5.tar.gz.sombernight_releasekey.asc
gpg --verify Electrum-4.1.5.tar.gz.sombernight_releasekey.asc Electrum-4.1.5.tar.gz
sudo apt-get install python3-setuptools python3-pip
python3 -m pip install --user Electrum-4.1.5.tar.gz
For more information refer to the Official download instructions for electrum.