We would like to use Power Automate flow to share every newly created project to certain user (or service account).

Unfortunately currently with the Customer Voice connector in Power Automate you cannot share projects. There are only two actions that can be done with the Customer Voice connector and those are "Create an invitation" and "Send a survey"

By sharing the project automatically with the "backup-user" or service account we ensure Projects don't get orphaned if the original Project Owner leaves the organization and hasn't shared the Project manually from the Customer Voice UI.