TL

““If i understand that Eden was where God dwelt on earth with perfect sinless people, then it is incomprehensible to think Eve ‘could’ have stayed in the garden as a sinner in the presence of God.””

That is a reasonable point. But the fact still remains that God addressed only the man to send him, not them, out of the garden. Perhaps, he wanted to see what the woman would choose to do, perhaps she needed to make her own choice in it, and also God likely knew that she would follow him.