Clean it up and take another picture. There is so much debris that I am having a hard time seeing what is what.

WHAT is going on with what looks like electrical cable?? Looks like insulation is stripped away where it is stapled to the joist. Surely not, but another reason that we need a better & cleaner picture.

Patching the hole is not going to be difficult.

In general, you want to seal the space. That means putting a piece of wood, then spray foam. For a cheap patch, you could get some styrofoam, which is easy to cut, and then use spray foam to seal it.

I think you are saying this pic is within a chase next to the fireplace, and through the hole is the basement? If so, then cut a 1/2" thick piece of drywall (2 pieces to negotiate the pipe) and screw from the basement ceiling. You can foam or caulk the gap depending on how close your cuts are. Your big box store probably has broken pieces of drywall for sale - you can cut it with a utility knife.

I would get some R-19 fiberglass batt insulation, which is about 6" thick, and simply pack it in the cavity around the pipe. It's not elegant, but it will do the trick with very little work.