Yes, you are correct. With the legacy PostgrSQL connector the entire connection string can be stored in key vault. but, it won't let you parameterize the connection string,
However, you can still parameterize the server name, port, database name, and user name by selecting the connection string option using the PostgreSQL legacy connector.
With PostgreSQL v2
Storing the connection string using the Azure key vault has been removed. This eliminates the need to create a linked service for each database on the logical SQL server. Instead, you can parameterize the properties such as server name, port, database name, and user name.
(by parameterizing the properties).
So uinsg Postgre SQL V2, you can't use the entire connection string in one key valut secret. This is by design.
You can refer to the following documentation for more information on how the linked service parameterization works.
I hope this helps.