Just guessing here but it sounds like the actual code is shared and the profile is probably just a new set of config, cache and data directories, sort of similar to having a different user home directory on a desktop Linux system.

I think it shares the APK, for example when you install an app from the app store the first time it downloads and installs it, but when you install it again from the work profile it doesn't need to download it.

That said if you are modding the app, if you change the app id (might be called something else), then android might be ok because it thinks they're different apps entirely avoiding the problem.

That's weird. I use Shelter, and I run different versions of Tasker. From play store on the work profile and from Fdroid on the home profile. Maybe it's a few apps that don't allow it?