She sounds very similar to how my dd was, though I did controlled crying when she was 5 1/2 months old which transformed my life tbh.
With babysitting, I took a gently-gently approach with her, the only times she spent apart from me was when someone took her out, in her pushchair, for a little bit, so she was less aware that I was leaving iykwim. And when I started more blatantly leaving her, it would be with a very cheery brief goodbye so that she wouldn't latch onto any feeling that anything was wrong. It surprised me how much easier it was than I thought it would be.
In separating from me when we were together, it got better gradually, slowly, the more mobile she got, and of course after having weaned her. I remember the first time she crawled voluntarily out of the living room. She looked back at me like "Woh, what am I doing??"
Sorry for ramble, you probably didn't want to know all that !