You seem to really want a serious answer, so you're going to get one. It'll be short and shallow, but I'll try. It all depends on how far you go, but if you want to go full throttle, then ...
Don't believe people when they tell you there's different types of people who can do this or that better. You can do all of that, if you just set your mind to it and learn it.
Yes, this can be improved. This is going to sound cheesy, but the calmer you are on the inside, the easier it will be to be thoughtful on the outside.
It is also really important to understand that, when you center your mind around coming up with something, you remove its ability to come up with something.
It is not possible to think about coming up with something and actually coming up with something. So if you catch yourself doing that, then stop that. Calm down. It's all good. Maybe the others are too fast and you're not actually slow.
I recommend you start meditating. You want to have deeper thoughts and want to express them, then you need to free up some processing power in your mind. Yes, that's how that works. Don't let people tell you otherwise. You'll achieve that with meditation. Daily. Twice.
Also stop having TV or music running in the background. If silence makes you uncomfortable, then silence is what you have to seek, to get rid of whatever is going wrong in you.
Next is breathing. Breathing, thinking and talking are connected. Most people's breathing is completely out of sync. For better inner calmness, learning how to properly breathe is of utmost importance. Meditation will help with that, too.
It's the norm that people can't rest just in themselves, with inner peace, but that's not normal, it's actually pretty fucked up.
The fact that there is a requirement for distraction means that there is something which needs to be distracted. Everything that prevents you from natural inner calmness is going to prevent you from deeply following conversations naturally and easily.
Also, besides freeing up your mind, it's important to actually understand that other people are supposed to be waiting for your response. When you feel forced into a hurry, then force yourself to be slow.
When you're in a conversation with other people basically reacting (almost) instantly to what is said, then they're not having deep thoughts, they're just mindlessly reacting. Even if it fits. The patterns they're expressing match the patterns they've heard. Doesn't really mean they're deep thoughts.
It is really helpful being able to spot who is actually thinking and who is just mindlessly reacting. You can learn that. Observe the face of the person. Eyes. How long it takes the person to come up with a response.
Deep thoughts require that things "settle" in the brain. They need to be processed. That takes time.
Which leads me to the next one. You should consider that you're pondering about things after the fact simply because your brain doesn't have time to actively work through things while they're a topic. See meditation.
Also, spend a lot of time with this: https://www.verywellmind.com/what-is-active-listening-302434....
Buy yourself a book about it. Look for an actually good book. Learn it, apply it, live it.
The lack of input in your post makes it hard knowing what the reason for your problem is. It's perfectly possible to figure that out via a conversation, but I'm not convinced this is a platform for that.
Well ... this was short. Not what I'd usually do. Report back in six months so I can see how you're doing. Feel free to ask any questions. I've probably kept this too short and simple.
(normally we'd be sitting together in real life for three hours talking about things, while i slowly transition you into a different state-of-mind. More focused, more "active listening", more "in sync with yourself", but that's not possible here. :)