Currenly tauri supports updater for Linux only for AppImage.
But AppImage works completly different from what tauri tried to achieve - it bundle everything into it and it makes it very heavy.
Also, AppImage doesn't work in some cases compared to deb which works pretty good even on multiple distros and even on arch based.
I think that it will be cool if tauri can support updater for deb in such a way that it will download the new deb file, request for password, exit, update, and relaunch ๐