Social Notes: no post title is saved when post is published

[jeherve]

This is a follow-up to #36718.

Steps to reproduce

1. On a site running the Jetpack Social plugin, activate Social Notes in the Social settings
2. Go to Social Notes > Add New
3. Publish a note
4. Log in to your site via SSH.
5. Fetch all notes: wp post list --post_type=jetpack-social-note

wp post list --post_type=jetpack-social-note
+----+------------+-----------+---------------------+-------------+
| ID | post_title | post_name | post_date           | post_status |
+----+------------+-----------+---------------------+-------------+
| 10 |            | 10        | 2025-04-03 09:36:14 | publish     |
+----+------------+-----------+---------------------+-------------+

Ideally, the post title would not be empty. Leaving an empty post title will cause issues like the one experienced in #36718, but also in other areas of the site, such as RSS feeds or Jetpack Stats.

I think it woudl be nice if we saved a default post title like we do to overwrite the display here:

jetpack/projects/plugins/social/src/class-note.php

Lines 192 to 205 in aa40ce3

	/**
	* Use the_title hook so we show the social note's exceprt in the post list view.
	*
	* @param array $title The title of the post, which we have set to be an empty string for Social Notes.
	* @param array $post_id The Post ID.
	*/
	public function override_empty_title( $title, $post_id ) {
	if ( get_post_type( $post_id ) === self::JETPACK_SOCIAL_NOTE_CPT ) {
	return wp_trim_words( get_the_excerpt(), 10 );
	}
	// Return the original title for other cases.
	return $title;
	}