Does NTE limited banner pity carry over to the next banner?

Yes, pity carries over. NTE limited character banner pity accumulates across phases — if you pull 50 times on Illica Phase 1 without an S-rank, Zhenhong Phase 2 continues from pull 50, hitting the 90-pull guaranteed featured. Note: limited, standard, weapon, and beginner banners all track pity separately. NTE has no 50/50 — any S-rank pulled is the featured character.