If I understand your problem correctly, pgAdmin4 runs in two-mode (Desktop and Server). In Server mode, users can sign-in using their credentials, but as the first step Administrator has permission to create new users (as normal or admin). Once sign-in using that credentials user can see the auto-discovered server and we have added shared server support https://www.pgadmin.org/docs/pgadmin4/4.26/server_dialog.html.
Is there a secure pgAdmin portal that can allow use of web based pgAdmin where users can register/sign-in and create accounts that can then allow access to PostgreSQL instances that are accessible on the internet via set credentials say via public IP as an alternative to pgAdmin installation on premise.