Add block types REST API. (#21065)

* Add block types REST API.

* Remove space

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Change comment.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Change comment.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Change title.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Change comment.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Remove array_shift.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>

* Change comment to 5.5.0

* Fixes.

* Formatting.

* More tweaks

* Fix lints

* Tweak fields.

* Feedback.

* Add block category.

* Feedback

* Add back composer.lock.

* Tweak descriptions.

* Add supports.

* Add unit tests.

* More tweaks

* Fix tests

* Tweak test.

* Reuse fake block

* Add in new fields and improve tests.

* Fix lint

* Reuse wp_error.

* Add more tests

* Improve asserts.

* Refactor permision check

* Add more tests.

* Remove unused method.

* Fix tests.

* Use correct name.

* Improve tests.

Co-authored-by: Andrew Duthie <andrew@andrewduthie.com>