Can’t see post status drop down for custom post type

There isn’t one.

In the classic editor the post status can be changed in the Publish box. There’ll be a small Edit link next to where it says “Status: Published”.

In the block editor, the post status is determined by the date and visibility set in the Status & Visibility box, under the Document Tab, and can be set to Draft by clicking Switch to Draft in the toolbar along the top.

There’s no dropdown with just a list of statuses in either editor.