If a modern ECU engine stops without generating fault codes then it's usually a problem which diagnostics sees as normal and has to ignore. E.g loss of the power supply, faulty ignition switch, loss of fuel aka the tank ran out empty or the immo coming on. Throttle control might be involved but I'd expect the engine to cut out back to idle? The way the engine cuts out is important. Totally dead quickly can be like turning off the key or the immo. activating, whereas dying slowly with some hiccups can be fuel related. As 2phast says the CPS, although it isn't quite in this category, but is effectively the ECU engine 'clock' on which everything else depends.
The OP has no error codes and diagnostics won't generate them so in theory live real time monitoring of the CPS would just show it stop. But in practice if there was a power source problem, it (and diagnostics using the same power source!) would stop anyway and you would be changing the CPS for nothing and still have the same fault. 2phast has experience of a CPS heat related problem but I've had them stop working at high rpm when the sensors and gaps become more critical.
ECUs are very complex devices and an intermittent fault in the ECU could be equivalent to a reboot, ignition on/ restart. I had this problem once on a non-V.W company car which was never resolved. The last time it happened was when I drove up to a junction ready to make a quick pull away, the engine died and I was nearly T boned. I refused to drive it again.
You can only diagnose this type of intermittent fault whilst it is ocurring regularly. If you dive in changing this and that without evidence, you risk hiding the problem, only for it to come back later. If the OP buys diagnostics I'm doubtful he would learn anything from this type of fault if there are no fault codes? All gas engines need fuel, air and sparks at the right time to run and that's where to start.
A regular garage or DIYer relying on diagnostics tools will struggle with this fault and I can see them racking up hours of labor? A good auto electrician may be a better option because all the symptoms point to a power source failure. A bad CPS or fuel problem wouldn't put out the dash display. Get somebody to check the main engine compartment fusebox for any burning and the loom ground terminal which is under the battery tray. Power steering stops when the ignition is turned off.