Anyone else not know how to reconnect with estranged parents?

I haven't spoken to my dad since about near the end of my 8th grade school year. He was very verbally and emotionally abusive and neglectful my whole life and one day I finally realized that I didn't deserve it and that I was old enough to decide who gets custody of me (my parents were already divorced way before) so I just stopped seeing him. I've been in and out of therapy for a pretty long time and I've mostly worked through my issues with him. I mean I'm still very much experiencing the long lasting effects of that abuse on my nervous system and it's gonna take a lot of time and work to get through that, but in terms of specifically how I feel about him I don't really care anymore. I can't say I necessarily "forgive" him because we never really talked it through but I'm not mad at him anymore. I don't feel mad at him specifically for the fact that I'm still dealing with the effects of trauma because although he is a big blame in that he's not the only abuser to blame and I feel like I'm mostly still struggling cuz of the second one and I'm already over the first one. I've also heard that he's started going to therapy to resolve these deep seated issues which I think is great. I'm well aware that the reason he was such an awful dad is because his parents were even worse. It's not an excuse, obviously it was never my problem as his child to deal with the trauma caused by his family, but I understand where it comes from regardless and I feel like if I can go to therapy to improve the things caused by familial trauma that he can do the same. I haven't actually looked into reaching out to him and seeing if he's better and if we can talk again though. I'm so extremely socially awkward and he's basically like a stranger to me because it's been so long and I've changed so much. I'm not even sure how aware he is of my name and pronouns. I know he's heard at least a little bit because one time in highschool I had to make a LinkedIn account for a career class and he found me on LinkedIn (presumably because I'm in his contacts) and sent me an article about finding transgender friendly work spaces. Whenever I think about speaking to him it just seems overall like I wouldn't really know how to connect with him. He's always been pretty rigid anyway, a lot of the time I used to spend with him felt like a chore that I had to complete because of a custody arrangement. Plus he lives in New York now and I live in Washington so I'd basically only be able to call him and I'm not very good with socializing without any medium for us to bond over. I need something we actually do and talking comes with it. That's why most of my life I've only ever had friends that exclusively talk to me in class as a distraction from class or friends that I game with. My dad and I hardly share any interests so when he was here he mostly just filled the schedule with outdoorsy stuff like hiking and camping but when we were home it was always so awkward. I don't think I could maintain a phone call with him even if I wanted to tbh. It just feels like I'm supposed to want him back. Like I definitely frequently wish that I had a normal loving relationship with *a* father figure but despite my knowing that he's trying to get better I never find myself wishing that I had a normal loving relationship with *my* father figure. I don't really resent him anymore so I thought that would mean I'd miss him cuz like it's not like I've never had fun with him I have lots of good memories with him, but I've never missed him since I cut him off. It makes me feel like I'm not very caring. I literally cannot seem to care for him. It always felt like I loved him because I had to love him. I don't think that's really love. I think my mom would like it if I did reconnect with him because I think she's always felt like it was her fault that I cut him off in the first place. The day I decided that she saw me crying because of him and she told me I didn't have to go. She meant that week specifically but it was the first time I realized I actually had a choice. I don't know how to feel about possibly reconnecting. I'm not really interested in reconnecting out of necessity I just wonder why it's not even the slightest desirable to me.