Abandonment Issues in reunited bio siblings?

*WARNING* *LONG POST* I found out I have a half-sister 13 years my junior in spring 2020 (the beginning of the COVID pandemonium). I contacted her via Facebook Messenger and we later would do periodic video chats, but primarily we communicated via Messenger. Initially, everything was great. We clicked right away, and we messaged each other multiple times per day. Her and I both grew up as the only child in our adoptive households, and we both became really involved in our new relationship (to the detriment of our in-person family relationships). She was in lockdown and had unlimited time to message back and forth, and I work a job that allowed me to be on my phone throughout the day. Every day, the person we had contact with first thing in the morning and last thing every night was each other. In retrospect, I realize that this was not a healthy, sustainable way of communication. The issues began very shortly after our initial contact. If I said something that would upset her, no matter how benign, she would go into "radio silence", refusing to acknowledge my messages for hours, sometimes days. This would drive me crazy, eventually I would have a sobbing meltdown. I would keep attempting to initiate contact, only getting a response after multiple attempts. The responses I would receive would be cold and sometimes mean-spirited. This same push-pull dynamic kept on happening over and over until June of 2021, when I finally decided I had enough. I called her out on her BS, and she responded in her usual fashion, accusing me of contacting her too much. I just got fed up and blocked her on Facebook. Throughout this entire time, I have had contact with her adoptive father. He and I share common interests, and we share light-hearted messages and jokes from time to time. Recently, I contacted him to see if he thought it would be worth it to reach back out to my half-sister. He asked her, and later that day, she e-mailed me. I was optimistic that we could maybe get to some normal relationship, but in our few interactions, her messages are very terse, and when I broach the subject of a phone call or video chat, she claims to be too busy for a phone call. I held back on responding, hoping to come up with an adequate response. Then, last Friday, her dad called me. In our hour-long conversation, he revealed something to me that I never knew. Ever since an early age, she has suffered from abandonment issues. (I forgot to mention that she was adopted at the age of 2 via a family friend, and had contact with our birth mother until her death in 1998. I was adopted via Lutheran Family Services and my records were sealed) He has encouraged her to seek counseling, which she refuses to do. I have just begun researching abandonment issues and their affects on adult relationships. What I've read so far reads like a script written about our relationship. The question I have for this forum is: Have any of you dealt with this issue and if so, what are some effective tactics to deal with the withdrawal/mind games/ etc.???