Sounds like she doesn't know what is making her unhappy and is frantically stabbing at things in order to make herself happy, and that includes you as a target.
Since she changed jobs and did all these other things that also didn't make her happy.
I had a similar situation and was dumped many years ago, and being told she thinks "I don't love her any more" or "I don't show her enough affection". The first one was untrue, but due to tiredness there was for sure some truth to the 2nd. However, was I unwilling to work on it? No, I was happy to work on it but being a new parent makes that really hard to do sometimes and so there was no convincing her. I was the problem, and I needed to go she determined.
While I've been happy on my own, my ex has had maybe 2 new relationships, one of which my daughter says "were arguing" - similar to our situation and certainly aligns with the blame game she tried to appropriate to me as "making her unhappy" and claiming everything I was doing was the problem.
Even after she was done with me, she wasn't done lambasting me for things I decided as a parent when our daughter was with me, even though these were minor things and my own responsibility.
It sounds to me like you won't be able to help this person to find out why they're unhappy and you won't be able to make them happy as they'll always be searching for something outside of themselves to make them happy.
I tried the same with my ex, to suggest counselling so that we could work on our issues for the best of our daughter. It all fell on deaf ears and I was told "it's too late for that" even though the problems weren't apparent to me until the end and she could have initiated it herself.
It was clear that this person didn't want to be with me. It was clear they were more interested in what I could provide financially and didn't want to actually know me other than that.
If I were you, I would let them leave if they want to leave, it's possible they could realise they do actually want you, but by then you might have moved on and found someone else. When you do split, make sure you make it a split and don't try to "be nice" by giving more than what you are legally required and as any child needs require in the hope this will make the situation better. Have some dignity and let them leave, and let them be by themselves as they want it.
In sitations like these, you have to consider "what if they'd died" - say if they were in an accident. You'd not have a choice over them not being there any more, so letting them go if they want to go is the best way to go.