Do the wood trim, in a thin strip that covers the side of the fireplace material. It’ll look fine.

NO drywall mud really. A thin piece of wood painted to match will be the best solution but really yhis should have been addressed at the start since the wall seems really wonky.A pic from further back might be helpful

You can mud your way out of this, but it's going to take a pro or a very experienced DIYer at least.

What about another strip of Quartz trim instead of wood? I think filling it look obvious. Like a wedge and will catch your eye. Hiding it with a trim piece on the edge would be better.