The Steam Deck can run Mass Effect Legendary Edition with almost no fiddling (at least if you bought it through Steam; Origin installs will not be covered in this guide specifically but most of it should still work if you can get the vanilla game running), but modding it is a different story. You have to run a windows program that has graphical issues without config changes, and give it access to the game directory because the game runs in a sandbox. I will cover how to get the ME3Tweaks Mod Manager running well enough to install and update mods, and lay out the known issues and limitations.
As a reminder, the modding tool set is built for Windows. Linux is not supported and will not be supported in the forseeable future. Linux specific bugs will very likely not get worked on. This guide is to help the small proportion of users who want to use the mod manager on Linux despite the lack of support and the issues and difficulty it will bring.
Most of this guide will happen in Desktop mode, but by the