Ubuntu 22.04 brought a lot of changes and features. Unfortunately, there are also bugs and issues.
Ubuntu 22.04 is missing the FUSE Library. Filesystem in Userspace (FUSE) is a simple interface for userspace programs to export a virtual filesystem to the Linux kernel. Without this library, Appimage won't work.
To resolve, follow these steps:
1. Open the terminal and use the following command to Install the FUSE library:
sudo apt install libfuse2
2. Remember to Allow executing file as program. Right-click on the Appimage file and go to Properties. Then go to the Permissions tab, and make sure to check the checkbox.
After that, all you need to do is double-click the Appimage file, and it should run smoothly.