Your list is in a Draft status, not visible to students and not prompting any action by the library, until you choose to publish it.
Once your list is ready, click on the My list is ready button in the banner at the top of your list. This will:
Your list status will change to Published and any items awaiting checking by the library will display as Library processing.
As each item on your reading list is checked by the library and is purchased or digitised, when appropriate, it ceases to display a status and can be considered complete.
You don’t have to finish your list to publish it and have the library check it. If you add new items to your list after it is published, they will be automatically sent to the library and will be visible to your students.
Should you wish to hide a published list from your students, from the ellipsis List menu at the top of the screen, select Unpublish list.