We cannot automatically log in to the embedded form or portal in the portal due to security issues that may arise. However, there is a workaround to achieve the same result.
In the form or portal you want to embed, go to the Share section and get the Magic Link.
In the users table you use for your main portal, create a formula field and paste the values here.
Go to the main portal's configuration.
Locate the Menu section and add an external link
Choose Embed in portal as the Link Mode.
Use Airtable Field in Link URL Source and select the newly created formula field.
By using this setup, you will achieve the same result of having users automatically logged in to the embedded form in the portal.
Additional considerations when embedding a portal into a portal
For a seamless experience while being embedded:
Make sure to turn off Show Portal Header (under Header)
Turn off Show Tables and External Links (under Menu)
Also turn on Hide Logout Button (under Profile).
This combination of settings will only display the table itself, which is exactly what you'd want for the embedded portal.
Limitations
Submitting an embedded form will not update the portal automatically, since the two are entirely separate. This means that any record you submit through the form will not show up in the portal until you manually refresh the page! If you want to create new records in your portal table, we strongly recommend using the "Create Records" functionality of the portal itself!