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

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:
https://github.com/Automattic/jetpack/blob/aa40ce3cd63102932a16a2d61b3af886b020a6af/projects/plugins/social/src/class-note.php#L192-L205

Start with projects/plugins/social/src/class-note.php around lines 192-205 and reproduce the issue by publishing a Social Note, then checking the result with wp post list --post_type=jetpack-social-note. Done means published notes have a non-empty post_title while retaining the existing display behavior.

Written by the indexing model from the issue text.