Hi @PowerAppUserCan,
I want to clarify one thing again, this is not a bug, this is by design.
I regret that this is not you want, however the guest user could only access to the shared app by clicking the web link from the invitation email or open it in mobile browser.
Just imagine, the internal users login the mobile device using the account from the same environment, however, the guest users login the mobile device using the account from their own environment which is totally different from yours. This is obvious that the shared app disappear in the app list.
Here is a trick from @Raynok1, this is not elegant, but could work on your side:
1.) Share the app as per normal process for an external user.
2.) Make sure powerapps is installed on the mobile device.
3.) Advise the external user to open the email from the mobile and select "open app". It should prompted them to either open via the browser or powerapp, Choose "Powerapps" of course.
4.) Sign in as per normal and there you go, it'll open in the powerapps mobile app.
5.) Swipe to the right, refresh your app list and you'll see the guest app in the list but all your other apps will disappear if you had other apps. Dont worry that's the "Odd" bit. Lets continue..
6.) On the gust app select the 3 dots or ellipses (not sure what its called) and pin the app to the home screen.
To get back all the other apps that you might of had, close powerapps mobile and reopen it (not using the guest app icon on the home screen).
Note that this is tested on a Android device, please check if this could work on your side.