Not trying to offend you but you said the coil packs, plugs, and wires were changed. Did you use the right plugs with the correct gap setting? Are all the plug wires fully seated? Did you use quality ignition parts such as AC Delco or NGK? Why did you replace these parts? Plugs and wires are maintenance items but coils don’t get replaced unless there’s a problem. If I’ve recently done work on my car and a problem shows up not long after I go back and check my work before going after something else. You seem to be concerned about how the exhaust looks. Did you remove a few spark plugs to check their condition? See if any of them are black with soot, wet with oil, burned, broken. There are some spark plug charts online you can use as a reference.

If you ruled out the ignition system then I’d check fuel pressure next. If fuel pressure is low the 1997 to 2003 C5’s have an externally mounted fuel filter on the drivers side frame rail at the rear of the car by the transmission that can be checked and replaced. Next I would check the fuel pump.

If the fuel system checks out then you’re down to an air management system issue, electrical issue, timing issue or as others have said possible restriction in the exhaust. With a random misfire code think in terms of components that effect the entire engine.

Again not trying to question your ability to work on the car but we all make simple mistakes every now and then.