It seems that Core WP expects the 'Add New' menu to exist in order to check if the user has the capabilities to add a new post.
This happens in user_can_access_admin_page if you want to take a look. For our case, the 'Add New' page should have a parent page for the appropriate capability to be checked in line 2178
I think that the only viable option is to re-add the menu and hide it with CSS.
Testing Instructions
Follow the steps in the linked ticket and ensure that the user can access the 'Add new' job listing page.
The user needs to have only the job listing related rights.
WooCommerce should not be active as Woo redirects the user to the 'My account' page if he doesn't have 'edit_posts' rights.
Plugin build for 3a72581fb398c9facbf9228286678381e9d738f3
Fixes #2673
Changes Proposed in this Pull Request
user_can_access_admin_pageif you want to take a look. For our case, the 'Add New' page should have a parent page for the appropriate capability to be checked in line 2178Testing Instructions