Kojima Productions will start full production on it after the Death Stranding 2 release, meaning almost 2 years before the next gen release. So unless they have support studios already working on it since years ago yes, it's going to be next gen game (who knows if crossgen).
Are they going to provide Sony feeback and suggestions for PS6? Yes, Sony -via Cerny- always asked their 1st and 2nd party teams, plus select 3rd party publishers about it for all their home and portable consoles before, so pretty likely will do the same with PS6.