Is Maha Bharani Shradh only for those whose ancestors passed on a Bharani Nakshatra day?

No — this is a crucial point. Unlike tithi-based Shradh days, Maha Bharani is a universal ancestral rite. Any family, regardless of when their ancestors passed away, can and should perform Shradh on Maha Bharani to receive the extraordinary spiritual benefit of this day. It is one of the very few Pitrupaksha days open to everyone without restriction.