[Visualize embeddable] Custom panel title not being saved for by value embeddables

[patodevilla]

Kibana version: 8.16.0

Elasticsearch version: 8.16.0

Server OS version: Elastic Cloud

Browser version: Chrome

Browser OS version: 130.0.6723.117

Original install method (e.g. download page, yum, from source, etc.): download

Describe the bug: After configuring a panel title and saving the dashboard, the data is lost after refresh. This issue is important since it deletes title configuration of existing dashboards.

Steps to reproduce:

1. Create new dashboard
2. Click "Add panel" and select "Aggregation base"
3. Create visualization and click "Save to library"
4. Click panel settings and give panel custom title
5. saved dashboard
6. reload dashboard. Notice how panel custom title is getting overwritten by title saved from visualization saved object.
   Expected behavior: Panel title settings to be saved

Screenshots (if relevant):

[elasticmachine]

Pinging @elastic/kibana-presentation (Team:Presentation)

[nreese]

I updated the re-creation steps to include details

1. visualization type "agg based"
2. saved by-value
3. with custom title. Saved object title is displayed instead of custom panel title.

[elasticmachine]

Pinging @elastic/kibana-visualizations (Team:Visualizations)

[nreese]

Added impact:high label because saving a dashboard with by-value visualize embeddables with custom titles will lose custom title state.

Added Team:visualization label because problem exists in visualize embeddable serializeState method. By value embeddables do not store titles state. This information is then lost on save.