Edit listing shortcode for email and webpage?

Including the listing link should be enough. In GDV1 the edit link will show on the page automatically in the sidebar.

Next time please post your V2 related question to the appropriate subforum so we know how to answer your questions.

The inline form with name and email is not intended to serve as a complete replacement for a login system.

V2 has a widget called “GD Author Actions” which you should place on the detail page so that a listing owner can edit their listing. Then in the listing published email you just send them a link to the listing.

If you do end up wanting the user to be able to retrieve their listing as attached to their account, then you use the GD Dashboard element or UsersWP options.

You can read about the account management options here:
https://wpgeodirectory.com/docs-v2/geodirectory/account-management/

You have not completed setup of UsersWP.
View the integration setup instructions here:
https://userswp.io/docs/geodirectory/

After login or reg you can direct users to their profile page, instead of the account page, which will display links to their listings once you have finished the setup.