Yes, of course.
The criteria says “The candidate must hold a degree of any of Universities incorporated by an Act of the Central or State Legislature in India or other educational institutions established by an Act of Parliament or declared to be deemed as a University Under Section-3 of the University Grants Commission Act, 1956, or possess an equivalent qualification.”
Manipal University (now Manipal Academy of Higher Education) falls under “educational institutions established by an Act of Parliament or declared to be deemed as a University Under Section-3 of the University Grants Commission Act, 1956” category. So yes, your degree will be valid for UPSC CSE.