I think it should have been done like this:

Here is a link that might be useful: undercut firplace

very nice. I'm not sure I grasp the technical issues of the undercutting. In my case, I don't think I had the hearth height to work with to do that. Your pics seem to have brick taller than floor. I also have some leveling issues with my hearth overall. Its not all the same height. Some cases the wood is taller than the bricks. Some its flush.

In any case, what do I do now?

Is undercutting brick or stone hearth typical for a flooring installer?

Undercutting is supposed to be standard. I'm going to be doing it this weekend with a floating floor I'm putting in.

In the first photo the trim piece appears to be higher than the rest of the floor. Is that not the case?

I'd be inclined not to fill in those cracks, I think it will look best the way it is.

That said, there are some tile guys who can make sanded matching caulk look really good, but tiles are a straight edge.

Here is a link that might be useful: tile wood transition with caulk

the trim is definitely flush with the floor. Must be the angle from the bad photographer. Its not exactly trim. Its just a floor piece turned the other way with a bevel on the brick side.

So is undercutting possible when the brick is lower than the hardwood? Its confusing me. THe former w/w carpet hid all this unevenness.