Project provides OData service as of now, that can be used to integrate with it.
Refer: https://learn.microsoft.com/en-us/previous-versions/office/project-odata/jj163015(v=office.15)
You can use the Rest APIs to integrate your app with Project.
https://learn.microsoft.com/en-us/previous-versions/office/project-odata/jj163048(v=office.15)
You may refer the below sample, in github, though it uses powershell, you can refer the concepts from the project.
https://github.com/OfficeDev/Project-Samples/tree/master/O365-Project-Online-REST-Samples
Hope this helps