Why does a chipped TDI engine run so much better without a catalytic converter?

Hello!
A question for the diesel experts.
I drive a 110 HP TDI (Golf 3) that has been chipped, and I haven't had a catalytic converter installed for about six weeks.
The original catalytic converter had broken off/rusted away at the flange, but I still had a spare pipe from the good old days of the VR6 engine.
Okay, so I'm just going for it, but an original Kat is quite expensive.
I was expecting less performance... supposedly, with actions like these, the software should be optimized.
But here's the thing: The car is running better than ever. Starting from the third gear, the difference is enormous – it pulls better, it responds better to the accelerator, and – what surprises me the most – it runs more smoothly and 'softer.' It even reaches its top speed faster now. How can I even compare it? I have been driving the same route for years, and I now know the top speed at every incline .
Last but not least, it also doesn't get as hot during longer runs at full power. That's something I can tell by looking at the oil temperature.
What the heck is going on? I'm missing the logical explanation for this effect.

'Any ideas?'

Hello,

I assume your old CAT was dense.
Adjusting the software when you have a different exhaust on a TDI is pointless; what's the point of adjusting it for? Charging pressure is regulated, but the exhaust system is not at all interested in the start of injection or the flow rate.

Best regards, Rainer.

I was actually referring more to the tuning for the missing cat (catalytic converter).
It was necessary for gasoline engines, and it did make a difference. However, I can't say how it works with diesel engines. I'm not very familiar with that either.
If the old catalytic converter was clogged (let's just assume that for now), would my car run better with a new catalytic converter? Or, to put it another way: Does it run worse without a catalytic converter?

And thank you very much for the quick response.

Hi, so I have a VW Golf 4 with a TDI engine. I also don't have a catalytic converter anymore, and I have a complete Group A racing exhaust system installed. Since then (and it sounds amazing), it runs much better! I've gained about 10 km/h in top speed, and it also accelerates faster! The Bosch service center near me said that the lower the back pressure in the TDI engine, the more power it produces, because the exhaust gases can escape more quickly, which in turn allows the turbocharger to work more efficiently, etc.
I'm planning to get my car chipped soon, let's see what kind of improvements that brings.

Best regards,
Stefan

115 horsepower according to the registration document .
121 horsepower with catalytic converter
129 horsepower, without catalytic converter and with exhaust system.

...the power that he previously used to 'force' the exhaust gases through the catalytic converter, you are now using for acceleration...

Hi,
Without a catalytic converter, the engine can be flushed more easily due to the lower back pressure, allowing more air to enter the cylinder. This results in a slightly 'leaner' mixture in the cylinder, which leads to lower temperatures during combustion. The engine also accelerates faster because the power that was previously lost to the catalytic converter's back pressure is now fully utilized for driving.
It's possible that you might have slightly higher power, but the torque will be a bit lower.