Site Editor: Template Part Areas are not exported

[anonymized_8769252]

To reproduce:

1. Open any block theme template in the Site Editor.
2. Add a Header block, with any content.
3. Save the template, and the template part.
4. Go into the database. You'll see the wp_template and wp_template_part post types, as well as the wp_template_area term all working well together.
5. Export the template and template part. Copy these to the theme, and reset any customizations.
6. See that the Header block is now a generic Template Part block.

Cause: During the export, the template part area is not added to the template part block.

The saved block might me something like <!-- wp:template-part {"slug":"header"} /-->, but it needs to be <!-- wp:template-part {"slug":"header","area":"header"} /-->

[audrasjb]

This was introduced in 5.9, not 5.9.1 :)