Hello Fredrik,
Thanks for the appreciation.
The looks of your Private Pages are coming from your single.php template file inside your theme folder.
If you want to have a custom template for client portal pages, duplicate that file and name it single-private-page.php
Or perhaps if you wish to have it look more like website pages, you can instead start by duplicating page.php
The Gutenberg editor for the private pages has been asked before and I am adding your request as well, so hopefully the development team will get to it at some point.
With the best of regards,
Gabriel