Move the node links bit from menu_ui to menu_link_node or a similar module

Problem/Motivation

As part of #2859270: Cleanup the entity <-> menu link integration → we want to move parts of menu_ui module into its own module.

Proposed resolution

Do it, see #2859270: Cleanup the entity <-> menu link integration → for the larger plan.

Remaining tasks

User interface changes

API changes

Data model changes