Unfortunately, this experience is still rather buggy. After adding photos, WordPress.com didn’t seem to be able to save drafts and it was also unable to display the most recent photos from the past week.

This seems like an issue with your site's connection to WordPress.com. It is not related to the Google Photos integration. If you'd like to fix this so you can use the WordPress.com Post editor and all it has to offer (including Google Photos), don't hesitate to contact Jetpack support with more details about your site, we will be happy to help!