Is it permissible for a woman to raise her voice in the talbiyah, based on what was narrated from Aisha in her saying: "Had he asked me, I would have informed him"?

The Sunnah is that a woman should not raise her voice in the talbiyah when entering ihram. This is a consensus among scholars, such that she should only make herself hear. It is disliked for her to raise her voice for fear of temptation (fitnah) caused by her. Therefore, the adhan and iqamah are not sunnah for her. Ibn Hazm differed on this, but the correct view is that of the majority. As for the story of Aisha (may Allah be pleased with her) raising her voice in the talbiyah, it occurred during the time of Muawiyah, and Aisha was old at that time. What is prohibited is a young woman raising her voice.