Lecturer here, and I would say it really depends on the setting and the content of the class. I tried different things that worked, pairing students to introduce each other for two minutes, then they have to present each other (small groups). Surveys with menti for large crowds, and I am also answering the questions (mix of personal/content/opinion questions to understand the general atmosphere ok the lecture hall).
In a summer school, I did something I really liked, the walking exercise. 3 rounds, 3 questions: students have to walk in the room, and when I clap they have to pair with the closest person and discuss the question. Then we share altogether. But again the content of the questions may really depend. The summer school was about transformations for sustainability, targeting PhD candidates. We were asking about an important event explaining why there were studying sustainability, one question was ‘what are you good at’ and the last one was ‘what do you think should be transformed to become sustainable.’
I am myself an introvert so I get that very much. The pairing is about trying to diffuse the anxiety. If I feel it is not working well, there are ways to mitigate the issue. For many exercises, interaction can be a nightmare for introverts. I was organising a role play in a master course and I know I would have hated that when I was a student, but I am trying to rely on my own experience to avoid huge mistakes and making people too inconfortable. It is important to read the room but also to experiment to see what works and not!