The SMAPI install instructions actually did a good job of explaining this. What you need to do to be able to run it, is to rename the "Stardew Valley.exe" to something like "Stardew Valley.exe.original". Then rename the "StardewModdingAPI.exe" to "Stardew Valley.exe". After that, it will run from the XBox App as if it were the original.
Right now it looks like it has a downlevel version of Stardew Valley (1.5), so I can't get it to run with any mod that requires JsonAssets or SpaceCore, so be aware of that. Unfortunately, this includes some of the more popular mods.