Hi Sreeram,
To create a new project in NEW UX, you need to create a project from Template.
In Classic UI, "New" and "New from Template" button are available to create a new project.
In New UX, you need a Template to create a project.
If you don't have access right for any Template, you will not create a project in NEW UX despite of Create Project Button is available.
Regards,
Shoichi