This is my first post, a nice light-hearted topic that resonates. 🥴
I personally had a very similar relationship with my mother. She ignored any attempts to lay down boundaries and stop the doom and gloom, despite me being persistent after therapy and learning how to create my own iron bubble so I wouldn't go insane. She was convinced she and I were so alike and had a special bond, since I was a vulnerable and depressed teenager. It was hilariously out of touch.
This had been going on for years, and I had been trying to enforce emotional boundaries for years. I put it down to ignorance.
Her actual nature was revealed when I had my own DD and I confided that I was struggling with post partum depression and was having doubts, and I asked for her to please stop bombarding me with messages about her own problems, since my poor mood was rubbing off on DD who was a few months old and I wanted to be present.
She snapped and said she had it far worse, with three DC under the age of 4 (I am the oldest) and she was disappointed in my attitude, since her time alone with me was the happiest she had ever been. It was so nasty that it shocked and upset me. I don't think I dignified it with a response.
Whenever I told her about my DD she would offer just emoji responses, but her problems were described in long essays. I refused to answer her calls when she asked if she could ring without context, because it was almost always an emotional dump.
I suppose my hope that she would change and actually begin to care about her only DGD prevented me from cutting contact right there two years ago. The final straw was about three months ago now, since she began outright lying, and honestly I do feel much better not talking to her. It's not worth the emotional drain.
If you try to enforce boundaries in kind, but firm, words and are persistent about it, and it doesn't stick, then reducing contact might be best for you. It's not a failure on your part. The kind of person who tries to get their own children to take responsibility for their emotions instead of dealing with them themselves isn't exactly reasonable.
Another thing is that she probably doesn't have any friends because of this behaviour. Don't put up with it just because you feel like a captive audience. She's taking you for granted.