My own experience recently was sort of similar, but not the same.
I had decided that I wanted to leave, and take the opportunity of retiring early.
Not the same as being offered another job, but nevertheless to leave.
Once I had made the decision to leave my motivation to perform my role dropped off dramatically. Not sure whether you might have the same energy in the role now, since you have realised that long term the role isn’t for you.
I would stil stay, short term , and look for something else.
The company are willing to look at you as a commodity, an under paid asset up until now, so I think you should be as cold hearted as well.
Personally, when someone handed their notice in with me, I alwayswishedhem he es for the future , never attempted to make them stay or change their mind.