I changed a wheel on my A3 several years ago after hitting a pothole and damaging one. No issue with TPMS.
As far as I am aware, VAG don't use sensors in the wheels. There are magnetic rings on the wheel hubs with pick up sensors positioned next to them. Rotational values are stored and any changes at one or more wheels indicates a possible pressure difference, ie a puncture. It's the same setup for the TPMS on my Skoda Octavia VRS.
Looking at the car from the front, from the left it's 1, 2, 3, 4.
1,2 and 4 are standard glow plugs. No. 3 is larger (more expensive) with a built in pressure sensor.
A wee bit further info. I had an issue on my Skoda VRS where the fans etc were working but no heat on passenger side vents. Turned out to be a thermistor in the vent pipe was reading high temp so hot air flaps didn't open as it thought it was already too warm. Replaced thermistor and all working again.
Info just in case someone else has a similar issue.
My 2016 gets around 46mpg average. Remapped from 150 to 190bhp. Only time I have seen a big mpg drop was on a car years ago was because a brake caliper was sticking on a bit. If nothing obvious with the engine, check the brakes are OK.
Shocking that they said its a wear and tear item especially when it involves fuel. If it was wear and tear, it should be in the service schedule.
They will know about this and deny its an issue. They did the same with my electronic handbrake issues for 2 and a half years until it was out of warranty.
Sounds like usual fob off from Audi. Very disappointing.
There used to be an issue with Skoda Octavias a while back with the geometry settings causing the rear tyres to quickly feather on the inside edges causing a droning noise. We had this on our VRS and it sounded like a failing wheel bearing. Skoda revised the rear geometry settings several years back and its been fine since. We did take it to the dealer twice and both times they set it incorrectly so we took it to a local specialist and it was fine. We use the specialist guy every time now.
Run your hand round the tyre edges and if its smooth one way and really rough the other way, they are feathering instead of there being even wear.
I have an h+r -50mm cup kit on the Skoda VRS (actual drop on the Vrs Was around 35mm) and it made a massive difference but the springs a slightly harsh on rough roads. Eibach springs are a bit more forgiving so I went with the Bilstein shock / Eibach Sportline springs option for the A3. It should lower it around the same 35mm drop.
Currently the A3 is not too bad but I find it a bit wallowy compared to the VRS. I would assume but don't know for sure that the standard suspension and 17' tyres would be even softer but don't have any experience of it.
I have the 18" wheels and sports suspension on mine. Its not too bad but a bit bouncy and wallowy on corners.
I am about to replace my suspension with a Bilstein B12 Sportline kit and front and rear Eibach anti roll bars to improve the handling and driving feel.
I have seen other posts about that happening. My warranty is expired now and none of 3 different dealers ever fixed the issue. They just deny all knowledge that there are issues with these handbrake (even when it stuck on in the dealership car park).
I hope you can get it sorted out.
If the EML comes on it should hopefully have stored some error codes. VCDS will read them (there may be someone on here in your area that has it) or a cheap ODB2 reader may show some if not all of them. You need the codes to start narrowing down what the issue is.