So all of them codes are linking to the ECU or the Lamber not getting the readings its expecting.
I had a similar issue on one of my R32's TWICE

First time is was the brake servo hose near the back end of the engine that had a split, the second time it was a faulty MAF sensor.
Thing is with VWs you can have something as small as a split in a hose which then causes multiple sensors to go out of wack.
Clear the codes off, it might be "pre PCV" and didnt have the codes cleared down.
If the codes come back that I would get looking into the entire system, start with the cheapest things first.
Check your Diverter Valve part number, if it doesn't end in "D" then you will have the Diapham model which is prone to splitting, the "D" version is the Piston version.
But here is a break down of the codes which should help you check things.
P0172 – System Too Rich (Bank 1)The ECU detects the air–fuel mixture is richer than expected.
Common causes:
- Faulty or dirty MAF sensor
- Leaking fuel injectors (on Mk6 GTI this is very common)
- High fuel pressure (faulty fuel pressure regulator or HPFP issues)
- Evaporative emissions purge valve stuck open
- PCV (positive crankcase ventilation) valve failure
- O2 sensor issues (usually front sensor)
P0441 – EVAP Incorrect Purge FlowThe EVAP system isn’t controlling vapor purge correctly.
Common causes:
- Faulty N80 purge valve (very common VW issue)
- EVAP leaks or stuck purge solenoid
- Blocked EVAP lines or charcoal canister fault
- Wiring fault to purge valve
P0303 – Cylinder 3 Misfire DetectedMisfire specifically on cylinder 3.
Common causes:
- Bad coil pack on cylinder 3
- Faulty spark plug
- Failing fuel injector (very common on Mk6 GTI)
- Low compression (carbon buildup on valves, worn rings, etc.)
- Vacuum/PCV leak affecting a single cylinder
If I had to take a guess, because you have already replaced the PCV, Sparks and Coils, its most likely going to be a faulty purge valve (N80) This is the single most common cause that can realistically trigger all three of your codes at the same time.
- It directly sets P0441 when it sticks open.
- When stuck open, it feeds unmetered fuel vapors at idle → rich condition → P0172
- That sudden enrichment commonly causes misfires, especially on one cylinder that happens to be most affected → P0303
On Mk6 GTIs the N80 is a very high failure-rate part. Cheap, easy to test, and easy to replace.
Simple way to test and replace the N80 purge valve, On the right side of the engine bay, attached to a hose coming from the charcoal canister. Looks like a small black plastic solenoid with an electrical plug. If you follow the hose coming off the intake tube (near the airbox), you’ll see it.
Remove the N80 valve from the hoses (very easy just hose clamps). Try blowing into one end of the valve with the valve unplugged (no power), it should
NOT let air through.
If you can blow air through it with no power → it’s stuck open → BAD valve. Buy a new one and replace it, the part number should be written onit somewhere. Should be under £50, just order it via your local VW or TPS (Don't use a 3rd party or used part)
You can also do a shake test, Not definitive alone, but helpful. Shake the valve about whiles its in your hand.
- Normal: It should click/ratttle lightly
- Bad: No sound, or sticky feel