When editing custom posts with the classic editor, the post author dropdown is empty (no authors to choose from), when the post type is managed by Access. The author dropdown is also missing from the Quick Edit UI.
(Support for the post author first needs to be enabled in the post type settings.)
We have several reports which suggest the issue arose after updating to WP 5.9.
The issue does not occur when editing posts with the Block editor.
Updating the Access settings so that the post type is not managed by Access offers a temporary workaround.