Rusty heating water with discolorations discovered.

You can see at the cut edge that the rust only forms a thin protective layer on the inside and practically does not penetrate into the body of the pipe. No worries.

Ok thanks.

Since we had the water damage due to the pipe rusted through on the outside, we have honestly been very unsettled.

I can well believe that you are massively unsettled after such damage. Normally, the good old iron pipes also hold up, and as wrote, there is nothing bad about the pipe in the picture at first glance. Even if faulty steel pipe should have been installed in your place, the entire floor does not have to be removed. The heating loops are made of composite pipe and that should be fine. There were strange composite pipes 30 years ago... I would wait for the insurance outcome and definitely install the sludge separator.

Composite pipes for underfloor heating or plastic pipes already make a difference due to the effect of corrosion. Starting from the composite pipes, no corrosion is to be expected. Therefore, a heat exchanger is omitted. So far so good, but still, there are often components made of steel installed, e.g., expansion vessel, bathroom radiator, sometimes just some kind of screw connection, etc. Then there is rust in the system, which in turn causes problems for the high-efficiency pumps because they are highly magnetic; the consequences can be imagined. The rust deposits on the heat exchanger, etc.

Prevents a magnetic sludge separator from causing damage to the high-efficiency pump.

The corroded pipe is corroded from the outside and not from the inside, that is now certain.

Does a magnetic sludge separator prevent the high-efficiency pump from being damaged?

100 points.
It also slows down or prevents corrosion and clogging in plate heat exchangers.

I also have to install one at some point, I missed it back then and only have a microbubble separator in there.