I totally understand where you are coming from. And as someone who isn’t much of a small talker, myself, I see how it can be particularly frustrating.
A huge factor in opening up deeper conversations with people is trust. And that can take some time to develop. Being consistent is key. It’s hard to develop trust when communication is sporadic. Also, sometimes the tendency is to want to talk to everyone but realize your capacity as a human and maybe pick a few people to focus on. Think about a few people you really want to develop a relationship with and make a point to check in consistently. Be sure to ask about things they might have mentioned in a previous conversation and show a genuine interest.
The environment in which you communicate could also be conducive to a deeper conversation. It’s hard to have a meaningful conversation when time is short, the group is large, or attention is being pulled somewhere else. Not saying deeper conversations can’t happen in these environments but think about being intentional with some one on one time. Create some space for the conversations you want to have.
Pray, pray, pray. Pray specifically for the people you want to talk to. Pray for eyes to see them as Jesus does. Pray for both of your hearts to be open to what the Holy Spirit wants so speak in and through you. Pray that you would see the opportunities in front of you and go into them with courageous humble confidence. Pray as you are in the situation. Prayer is crucial.
You might also find this talk from Vince Vitale helpful
May the Lord continue to use you to draw people to Himself, Anna. May you rely on His strength and wisdom and be attentive to the Holy Spirit. May He prepare the hearts of those you interact with and reveal more of Himself in this whole process.