Leaving for compensation is absolutely a valid reason. Again, though, the same rules apply. Express to your employer you have received a job offer at X% more, with X improved benefits, and would gladly stay for a match. The worst they can say is no, correct?
Either way, the original conversation was about issues with the employer/manager. Not necessarily compensation.
I feel like that’s a bell you can’t unring though. What if they say yes? How can an employer possibly trust you don’t just go looking for an even better deal in a few months?