You should also submit this problem to the Microsoft Skype team and the answer may not please you, these morons suggested to me a few years ago to use a PC for the pro account and a phone for the personal or the opposite . It may have changed since, contact them. Otherwise, with the Zebra support team we had found an alternative solution, you use the Android version in one profile and you add chrome in the other profile and you use the other Skype account via the Web
S10 was with Android 9 I believe, it was the beginning of personal and professional profiles for Android and Samsung was ahead of this point long before and on screen sharing where you could have two Active/Active apps that didn't still does not exist on stock Android. Going back to Twin App with Android 11 or 12 yes it is normally possible, I think there is a Bug with Asus since 2 or 3 Android 11 firmware with the management of personal and pro profiles, clearing the cache no longer works (it goes to zero but if you go back to it it puts the old value back) and it is no longer possible to stop certain applications.