There is an email notification for "The status changes on a project I'm on" that you can activate with Setup, however, keep in mind that email notifications are global settings and this would activate the notification for all users within your system. Likewise, you cannot pick and choose which users to notify on a project - anyone who is listed on the People tab of the project (Project Users) would be notified.
If there is action needed from the requester once the project status moves to Out for Review, you may want to consider:
- tagging that user in an update/comment to let them know of this status change
- create a report that is pinned to this users' global navigation (or attached to a dashboard and set as the default landing page) that surfaces Project Status in a column with a column rule added for something like, if Project Status > Equals > Out for Review, highlight red
