AppImages are supposed to be able to handle all of that and I have used a number of them that do. In the case of Tauri though it seems nobody on the framework team knows Linux well enough to fix the build process to not constantly break as libraries update on the GitHub Ubuntu VMs or to make all the required dynamically linked libraries get included in the AppImage. And finally most of the downstream app developers have never written an app for Linux and chose the framework expecting it to solve the problems it clearly isn't.
The main issue being that they're dynamically linked binaries, which is exactly what you want to avoid for their use case.
Using packages from your favourite distribution is usually your best bet.