For “Invite people” it is currently possible to “Add these people to this project”. Only one project can be selected.
It would be great if you have checkboxes to select mutiple projects. This way you do not have to add these people to the other relevant projects after they registered.
Instead of checkboxes it would be a good user experience to have the dropdown and an “Add” button. When button gets pushed, the project is visible as a label that can also be deleted again. If there are more then x projects and the dropdown gets to long to view, don’t show all projects (list the first and say “x more projects” and add a search field to the dropdown (https://www.w3schools.com/howto/howto_js_filter_dropdown.asp).