Deleted menus are still referenced as available menus on content types and cause an error when content is edited

Problem/Motivation

When a menu is deleted, which was previously referenced in a node types' available menu settings, an error is thrown and "parent item" select field contains invalid options.

Issue is still present in 8.2, 8.3., 8.5.4

To reproduce

Required modules: menu_ui, node

1. Create a menu.
2. Create, then edit a node type. In Menu Settings -> Available menus. Select the previously created menu. (Figure)
3. Save the node type.
4. Delete the previously created menu. (Figure)
5. Create or edit a node entity, with the previous node type.
6. The following issues arise:

An error is thrown on a node entity edit form:

Notice: Undefined index: MENUNAME in menu_ui_form_node_form_alter() (line 279 of core/modules/menu_ui/menu_ui.module).

And invalid parent item select options:

Proposed resolution

Add soft dependency from menu configs to node type.

Remaining tasks

Patch, tests.

User interface changes

API changes

Data model changes