Step on the gas just a little the engine will stall

It sounds like the fuel pressure may have problems. Not just the static fuel pressure at idle, but the fuel pressure as it increases when changed by the fuel pressure regulator. As the car gets boost smaller changes in throttle position are actually harder to manage than large ones. This is because the fuel curve changes so drastically per throttle position change. Instead of being more linear the curve is logarithmic.
Besides the fuel pressure regulator, the throttle position sensor could be contributing or at fault for the issue as it is harder for it to detect smaller changes in throttle position as well. It uses a voltage signal which tells the ECU what to change with the fuel curve, ignition curve and if so equipped with electronic control of the fuel pressure regulator the fuel pressure and the boost control.

I am providing you with the troubleshooting checklist from the service manual for the car. It has the aforementioned items on it.

Did they ever tell you what trouble codes came up when they ran or pulled the codes? Even though there is not a check engine light trouble codes can still be stored when they pass a certain specification level without tripping the Check Engine Light. Once they are further out of spec and can cause a NO RUN or NO START situation, they then trip the Check Engine Light. So, no matter what the codes should be checked. Make sure they did so and ask them what they came up with. Then go over the list I am giving you and ask if all these issues were addressed. Do not get hung up on the title of the list as your issue still falls under this category. Don't share the title of the list with the repair shop so they can't say that the list is not related to your problem.

Also, the fuel pressure should be checked manually with a gauge. This as opposed to the repair shop telling you that the fuel pressure is fine because there is not a fuel pressure trouble code. It is still best to check it manually as it will be tested in a state without the vacuum or electronic signal that changes the pressure with engine RPMs and other parameters. This is a static test of the fuel pressure regulator. Then it is also tested with the change signal and sometimes tested at different RPMs to see how the regulator reacts to RPM changes.

So, I would ask that they do that. The throttle position switch should also be checked with a multi-meter even if there is no trouble code as it could cause an issue because the problem is with such a slight throttle change that it should be looked at while the throttle body is slowly opened and closed. The ECU only throws a code when Idle or Wide Open Throttle values are out of spec.
All the issues should be inspected manually whether they throw codes or not for said reason, but the above two are very likely to be the problem or at least have to be completely ruled out as they are, "Ground Level" sensors and controllers that affect engine performance with throttle changes.

Let me know how things go and I will keep an eye out for your response and reply ASAP.

The torque converter will cause issue like a feeling that the car, "Slips" between gears or when taking off. It can also cause a shuddering noise a it can be felt. Solenoid cause problems between shifts as if it is hesitating to shift into the next gear and can cause a sensation of slipping while shifting. These are often worse in both cases when shifting into overdrive, if so equipped.
If you scanned codes and nothing came up you can still have low fuel pressure and you have to check it manually. You can get a fuel pressure gauge on a loaner basis at Advance and Auto Zone with a deposit. The kit comes with adapters for the test port which is on the fuel rail. I am providing you with fuel pressure test procedures and specifications for pressure.

The other parts that can cause timing and fuel curve issues, fuel curve problems can seriously rob performance on turbo cars, are the crankshaft and camshaft position sensors. So, I am including the test procedures for resistance, air gap and voltage, those don't all apply to bot, to check them for basic issues. If they appear to have any physical damage they might need to be replaced as well.

The Throttle Position Sensor can be tested for voltage at closed and wide open positions. However I could not find the specifications. Generally closed is at or near 0 Volts and wide open is 3.5-4.5 Volts. You may have to ask a dealership to look up the specification as most times it does not get tested, just replaced.