This is an interesting topic, and nope, I don't think what you are talking about is all that unique.
We live in a society where we are constantly turning channels, we have addicitions to our phones and will stop mid conversation to check them. We have so much data available to us as well.
I think you are actually talking about two maybe three separate concepts.
1. Some of your unfeeling is you have likely learned to numb your feelings. I was very numb surrounding the affair time and could not connect with feelings that would have made sense. Typical one: I love you but I am not in love with you. On the surface, what does that even mean? It means we have numbed something in order to do something else. To me the process of awakening some of those feelings was very painful. I found Brene Brown's Rising Strong book to be really a good one, she talks about how when we numb bad feelings we numb good ones. I think waywards in general overvalue good feelings and want to avoid bad ones.
2. You could be like my husband (and this is the one I am not sure and why I said maybe 3 things). He has this inability to understand his emotions or to rank thinks. Like, once he was having these feelings of depression and would get overwhelmed throughout the day a few moments at a time. He went and read about it and told me "I can't differentiate if during that time I am feeling sad, or anxious, or something else" He doesn't know the difference. And, when I say ranking, I will say "what was your favorite part" or "what's your favorite____". He freezes up with that, because he has two modes he likes it or he doesn't. Yet, he's sensible and very emotionally mature and he handles situations very well. He's very in control. So, I don't know if that's something that you are describing, but I thought I would throw it out there in the case it's suitable.
3. Mindfulness. I think as I said in today's society we don't have this. There are a lot of things I have done and still do to tap into this. The reason it's so important is because we can't feel joy if we are mentally in the past or present, and if that's the case it's likely that you can't feel anything else.
I would recommend reading "The Power of Now" by Eckhardt Tolle. He talks a lot about how to objectively look at your thoughts, meditation, and a lot of the topics I think you are looking for answers on. It's not a breezy read - I had to read it in segments and absorb it, but it really does help me cope in situations better and has really made me aware of what being in the moment is and trying to practice being present more consistently. I also recommend a yoga practice. I hated yoga by the way - but I found that if I just do a 15 minute video 5 or 6 days a week it brings a feeling of wellness to my mind. I practice meditation on and off, and I am not a good meditator but in the thick of the worst of my depression and shame it was exactly what I needed.
I don't know if you exercise, but I find that to be a meditation of it's own. If I am running, I have to focus on my breathing, my cadence, my direction. I can't let my mind wonder. It creates a lot of endorphins for me and it helps boost my confidence and energy. I have a hard time feeling blue on a regular running schedule. I started with a walk to run program and I think that might be something that would help you with anxiety with some of the new time you have on your hands.
I don't remember if you were one of the ones pining for your AP (you came here originally in a crop of them), but I know that you are now on your own, just out of curiosity where are you with that?