Is it permissible to inform a neighbor that she is the cause of committing sins due to her excessive talking, or is it better to continue to shun her gracefully without informing her of the reason?

Abandonment should only occur when influence and benefit are no longer possible. When you communicate with your sister, take the initiative to offer advice and encourage truth and patience, and occupy your time with what is beneficial. If you notice she enjoys talking about others, explain to her the dangers of backbiting and gossip, and the importance of thinking well of others, and engaging in Quran recitation, remembrance of God, and studying Islamic knowledge.