Unlike snaps and flatpaks, Appimages aren’t containerized or sandboxed at all. They are only used to bundle (some) dependencies, so you don’t need to rely on packages provided by your distro’s package manager.
You might want to look up what Appimages are as well as what containerization is. To help I have found the following.
AppImage aims to be an application deployment system for Linux with the following objectives: simplicity, binary compatibility, portability, distro agnosticism, no installation, no root permission, and keeping the underlying operating system untouched.
As stated Appimages are containerized/sandboxed as it prevents needing to install any files on the OS.
Containerized applications are applications run in isolated packages of code called containers. Containers include all the dependencies that an application might need to run on any host operating system, such as libraries, binaries, configuration files, and frameworks, into a single lightweight executable.