I'm guessing those are probably separate problems. The IAC is faulty, and something else is leaking coolant.
As far as the situation in total, with all of those problems noted, it would be difficult for the shop to know where to start first. If they knew beforehand the cat had failed and debris had ended up in the cylinders, I expect they'd have informed the owner before any repairs ensued. But apparently they didn't know this, so they went ahead & replaced the ECM, fixed the coolant problem, replaced the spark plugs, and the relays, only for the owner to discover the oil usage problem which the shop ascribes to the cat breakdown. No shop is going to let a owner drive a car away with worn through brakes. I feel for the OP, but I don't see that another shop would likely have done anything differently.
In retrospect, for a 15 year old vehicle with close to 200K that needs a new ECM, has a coolant leak, completely worn out brakes, spark plugs, all that indicates normal preventative maintenance is likely well behind schedule. The best course of action in that situation is probably not to immediately start fixing everything that is known to be broken. Instead basic engine testing is probably the first objective, a compression test, cooling system pressure test, possibly a cylinder leak down test. Whether all that would have resulted in a different outcome however, hard to say. It depends on what those test results were and interpreted.
So what's the OP to do? hmm .. I don't think laying blame on the shop is going to get the OP anywhere. Probalby best to try to keep the shop on the OP's side. Ask if it might be possible for a machine shop to fix what's broken w/ the engine insides. Or what it would cost to replace the main block or the entire engine with a used one from another wrecked.vehicle. the shop might be willing to eat a portion of the cost, given what the OP has already paid. And the OP vehicle does have a new ECM and repaired brakes. There's the issue of the cat replacement expense to consider still. So it might make more sense to just give up, sell it to a junkyard, and buy another vehicle.