Return `post_types` field in templates REST API

[oandregal]

While working on the site editor templates screen, I realized we don't expose the post_types field through the templates endpoint ​https://developer.wordpress.org/rest-api/reference/wp_templates/, though it's one of the parameters consumers can use to query it.

In the dataviews-powered page, we want to expose this information so the user can filter templates that are intended to work with a given post type.

My suggestion is to expose this new field through the existing templates REST API endpoint.

[oglekler]

@spacedmonkey can you, please, take a look. I have doubts that we will be able to make in into 6.6, but it looks simple enough and quite reasonable to have. Thank you!

[spacedmonkey]

@oandregal can you add a unit test for this change.

[oglekler]

We have 3 hours until the commit freeze before Beta 1 release and no Unit tests. I am rescheduling it to the next milestone. Let's make it when Trunk will be open for enhancements again, without waiting for the last moment. Thank you 😅