We cannot automatically log in to the embedded form in the portal due to security issues that may arise. However, there is a workaround to achieve the same result.
In the form, go to the Table & Login section and get the login formula.
In the user table, create a formula field and paste the values here.
Go to the portal.
Find the Menu Item section
In the menu where you want to embed the form, use Airtable Field in Menu Item URL Type and select the newly created formula.
By this setup, you will achieve the same result of having users to be automatically logged in to the embedded form in the portal.
The same applies if you are embedding a portal within a portal.