Nav block/editor - can't save a post-format

[getdave]

Currently you cannot save a post-format in navigation editor. It is very much related to #31380.

Essentially we are storing an non-numeric object_id because the REST API endpoint returns non-numeric IDs for post-format search results.

As per the existing menus screen we should store the taxonomy term ID (which backs the post-format) as the object_id for nav_menu_items.

To do this we need to make sure the /v2/search endpoint returns the term ID for us to work with. See #31380 which shows what the REST API currently returns.

How to replicate

This takes a bit of setup:

1. Activate a theme that supports post-formats, like Twenty Thirteen
2. Create some posts that use a post format like quote or gallery
3. Enable the navigation editor and create a new menu
4. Insert a post-format link (points to the post format archive). Note that this should be using the post-format variation:

post.format.mp4

A custom link works out okay but we should avoid the 500 here:

500	Sent values

Originally posted by @gwwar in #31004 (comment)

[Mamaduka]

Closing the issue since the editor is no longer maintained and has been removed from the project.