Sports - a lot of state schools have these as well or they're local leagues too (athletics is a good one as local running clubs have a junior division). This really helps with confidence and discipline and doesn't need private school. Think of all the successful athletes from the state system.
Travel and culture - I went to private but learnt everything I know from my parents who took me to the theatre/concerts, introduced me to new foods, watched the news with me, dinner table conversations not stuck in front of telly. This doesn't have to be expensive but does need parental effort.
Hobbies - private coaching for whatever this might be. Music, art, coding etc
Tutors if they're struggling with the academics.
Don't shelter them too much. Doing a summer job, travelling places on their own - all this builds confidence.
Everything else evens out at uni and the workplace. If your child has a curious mind, discipline, some skills and hobbies, and understands different perspectives and ideas - they will do well in life no matter the school. On my City grad scheme 20 years ago there were plenty of kids from the state system as well as the assessment/interview process focused on team work, knowledge of the world, quick thinking and communication - which isn't on any curriculum. Private school helps with leadership, confidence, sports but honestly this is more about affluence rather than anything inherent.