Plumbing – run PEX through PVC pipe embedded in a concrete floor with radiant heating

You're not going to like the answer, but the way to properly fix this for good is to break up the concrete, cut out and replace the damaged section of pipe.

There are a variety of ways you could break this up. A sledge hammer, a hammer and chisel, a SDS drill with a chisel bit, or a larger chisel like a Brute. If you have a ton of time on your hands, you could use a standard hammer drill and drill tons of little holes around the area to remove and then break it up with a smaller hammer and chisel. The concrete should not crack outside of the immediate area you are working on. As for the pipe, yes you might damage it further but you need to replace a section anyways.

Once repaired you would add new concrete and replace the finish (hard to tell from the pic).

Any other fix is unlikely to be permanent or without compromise.

PVC pipe embedded in concrete should be fine under most codes I've seen. You'd need to sleeve something like black, galvanized, or no-hub iron pipe, but PVC and ABS are impervious on any reasonable timeline (~hundreds of years.)

You could have your inspector come through before the pour to check out your plumbing permit if needed.

And the diagram worked great, I think I understood exactly what it was conveying.