When I (an introvert) was in elementary school (many years ago!), I was in Girl Scouts. It was good for me because there were lots of other girls around my age and we had activities that we did together (e.g., making crafts, camping, working to earn badges). It helped to have some structure so that I didn't have pressure to think of something to say out of te blue.

I also enjoyed art and took drawing/art lessons during the summer. That worked for me because it was doing a solitary activity around other people doing the same thing without the pressure to talk. I also took ballet lessons. There are other girls and she'd have to operate within a group, but there isn't pressure to have conversations. I wish gymnastics had been available to me when I was young. Maybe she'd like that. The focus is on developing skills, but interactions with others just happen. I guess I'm saying to create opportunities for her to learn how to interact with others in various social situations where there is a safety net.

I love that she enjoys reading and writes poems! Maybe she could read a story to a younger child once a week. This could let her feel in charge and yet helpful. Although it would be with a younger child, it still is an opportunity to learn conversational skills before and after reading.

Are their neighborhood children that go to her school or that she sees often? You could ask her if she'd like to ask that child over to cook something together (e.g., bake cookies or make pizza).

What she "absolutely does NOT need" is pressure or criticism about not being social enough. (I'm certainly not sugesting that you have done that. In fact, it's impressive to me that you've written here so sensitively about her needs!) This kind of pressure only made me retreat further in social situations as a child.