macOS Ventura introduced a seperate pane for Login Items. It's divided into to sections: Open at Login and Allow in the Background. In the first section the user will see DisplayLink Manager application entry if automatic app autostart is allowed. Installing Login Screen Extension will add one item to the Allow in the Background section under DisplayLink Manager.

When the user adds Login Screen Extension a notification will appear: 

In case of any problems with using Login Items pane while uprading from version up to 1.8.0 alpha, please use provided DisplayLink Software Uninstaller and install the latest DisplayLink Manager app.

In case of any problems with using login items pane when upgrading from version up to 1.8.0 alpha, please use provided DisplayLink Software Uninstaller and install latest version of the Displaylink Manager.