Less power than it should/bogging motor?

It looks like the valves on a signal overhead cam are adjustable by a lock down screw, but the dual overhead cam, the valve lifter actually needs to be measured like a shim to adjust the valves, those are a pain. But I'm sure you would be setting misfire codes if the valves were that far out of adjustment. Let's hope it's the rear converter.
How did the front 02 look? Was it covered in soot?

Yeah, they are difficult to work on being a box engine, we used to just pull the engines to do the head gaskets, there was a huge head gasket recall back in 2002 I think it was. As well as a Recall for ECM programming, I must have reprogrammed 500 vehicles, lol. But I agree the new ones are really difficult, especially with the huge timing chain on the dual overhead cams, that was 20 years ago too.
One other thing I was thinking of is checking the MAF sensors g/s (grams per second), it should average around the size of the engine. So a 2.5liter should roughly be around
2.8-3g/s at idle.
Try the VE test as well, on the website page for the test at the top it gives instructions on exactly how to do the test. It can save a lot of time when diagnosing low power issues like this with just scan data. And give you direction to test pretty fast.

The highest RPM you hit with a quick wide open throttle run. You record your live data and input the numbers that occur at that highest RPM. That way you're getting the max load on everything. The scan tool should be able to record a certain amount of time, and then just scroll through the live data until you come to the highest rpm achieved, stop there and use all the data sensor numbers from that point, if that makes sense.

Yeah, you need to find a back road somewhere you can do a wide-open throttle run, just once and record the data. The instruction on the page explains things, you have to be moving so you put a full load on the engine to get the max air flow it will take in and that's how it calculates the maximum volume of air the engine can pull in.

The 2nd picture looks a little odd. But if that reading of 8psi back pressure is correct, something is not right. I would go through and do the full VE test to see what kind of numbers come up. With nothing setting any codes and the extreme lack of power you described, we need to know if there is correct air and exhaust flow. Even the MAF sensor will tend to read low with a converter issue, less air is going to enter the engine if the exhaust can't escape. I don't really rely too much on temperature tests for converters because it's just not a definitive answer. But a VE calculation will give you more of a direction. Something is causing that high back pressure. There shouldn't be more than 1.5 to 2 psi of back pressure. Has this vehicle had the cats replaced before? Meaning is there possibly broken up sections of an old cat stuck in the muffler? Some shops forget to check the rest of the exhaust system after replacing a broken-up converter, and pieces end up downstream in the exhaust.

Okay, sounds good. Let us know what you find. I'm surprised they don't have an oxygen sensor behind the 2nd cat. Service info clearly calls it a rear catalytic converter.

They just do all their fuel corrections with the front cat.

Yeah, that is still way too high, you can see with the tool, they even show the max limit of back pressure. Thats what is causing your bogging down and lack of engine response. Even at 2psi I worry. Glad you got the right kind of kit though that will come in very handy in the future. But I think you should drop the exhaust from the bolts at the rear of the 1st converter and see what's going on. You have a lift to work on, so that's a huge help. Most of the time I'm working on the ground during mobile calls.
Did you try raising the RPMs as well, and did the back pressure increase?

Even so, at idle it's too high. It looks to be reading about the same as from behind the front cat, so it has to be the rear one. But once you unbolt the rear of the front cat, have someone help you just lower the entire exhaust, they are easier to take down that way. That's how we would do it at the dealership.