Delete only theme-related caches when saving changes

[t-hamano]

Related to #655, #654

This PR changes how the cache is deleted when you save changes to a theme:

• Delete the database cache as well as the object cache
• Delete only the theme cache, not all caches

Delete the database cache as well as the object cache

As I understand it, the wp_cache_flush() function deletes only the object cache. On the other hand, the pattern uses the database cache via the Transient API (Source).

Therefore, I think that wp_cache_flush() cannot completely solve the problem reported in #655.

In my testing in the local wp-env environment, the content did not appear in the editor canvas after saving a modified template unless I deleted the database cache or changed the value of the DEVELOPMENT_MODE constant to theme.

Delete only the theme cache, not all caches

wp_cache_flush() function deletes all object caches. Therefore, it may have unintended negative effects on sites that are trying to improve performance by using object caches.

WP_Theme (wp_get_theme())->cache_delete() method properly deletes the object cache for the theme and the database cache for the pattern (Source).

Testing Instructions

First of all, I would be grateful if you could confirm whether the problem reported in #655 still occurs in the wp-env environment and test whether this PR solves the problem.

If this PR is useful, we may evaluate the effectiveness of the wp_cache_flush() function used in other places individually and replace it with a different cache deletion method similar to this PR.

The video below shows that the issue reported in #655 still occurs in the wp-env environment.

a164276e19a6881b67d82c56cfc5bb8b.mp4