I have been on sea princess 4 times. People wear jacket (linen often)and tie in the restaurants on smart casual nights.At the very least a tie is required. Open neck shirt in Pizzareia or horizon court buffet though the Horizon is often cold !
No jacket only required on formal night.
We have just returnsd from 2 weeks on sea princess, a jacket is only required on formal nights a suit jacket wil do. However the buffet supplies excellent meals if you do not wish to go formal,but it was nice to try i.