AutoText entries must be stored in a template (*.dotx or *.dotm). I think you're working in a document (*.docx or *.docm) file. You can use the File > Save As command (shortcut F12) to save a copy of the document as a template and work on that. While you're creating the AutoText entries, either have the template itself open, or work in a document based on the template; that will make the template available in the Save In dropdown of the Building Blocks dialog.
Each time you need a fresh copy of the form for a new project, double-click the template in File Explorer, or right-click the template and choose New in the menu. That will create a document based on the template.
In the article that Suzanne linked to, steps 9 and 10 of the "Create a popup list" section explain how to create the AutoTextList field without the Fields dialog: Press Ctrl+F9 to insert the field brackets, and type the field code between the brackets.
If you prefer to use the dialog, the "New value" box that you see in your screen shot specifies the text that will be visible in the document (the "Choose a project type" in my example). Then you need to click the Field Codes button in the bottom left corner of the dialog and add the \s "Project" switch (and optionally the \t switch to change the tooltip text) in the Field Codes box.
I also recommend clearing the check box for "Preserve formatting during updates", which adds a fairly useless bit to the field code.