What’s the benefit of having it show up in the launcher anyway? Sure you’d have a central place that allows you to launch all your versions. Not sure how many you have but for me it’s rarely more than two (e.g. 4.26 and 5.2 currently). You probably don’t want the custom version to be updated through the launcher either especially if you have custom changes in your engine.
If your working on a specific project the typical workflow would be to open that project directly. So you almost never need to launch into the “Unreal Project Browser”. And for any .uproject file you can right-click it and run “Switch Unreal Engine version…” from the context menu then select the installed or source build you want.