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from my understanding, you can run widebody sizing, so yes 325s will fit. How they will look or work on your wheels depends on the specs of the wheels though (width and offset).
You can do a quick search on tire rack for GT3RS tires but that is for the GT3RS wheels. I think the GT3RS wheels are 19x8.5 and 19x12 with a lower offset than the regular GT3 wheels.
There is a GTS for sale in the classifieds right now that was running GT3RS wheels with 325 rears and 245 fronts from my memory. However, they may have switched back to the OEM wheels.
This may or may not be the car: https://www.spmsracing.com/blog/2018.../carerra-4-gts
I would also recommend getting an alignment at minimum if you go up to 245f/325r.
here is the car. I am not sure if it is the same as the car above but note that there are OEM GTS wheels on the car now. If my memory is correct, it used to have more aggressive wheels and tires. https://rennlist.com/forums/market/1169231
one last thing I thought of that you may already know is that if your wheels are OEM, you can see the width and offset pantographed on each side of the valve stem.
You can use that information to search what tire sizes are appropriate or not.
If your objective is to fix the tucked-in look of the OEM RS Spyder wheels, you'll have to go with either GT3RS wheels or aftermarket wheels that have more aggressive offsets. Simply going with a 325 rear tire won't do it. Here is mine with GT3RS rear wheels and 325/30-19 tires, and GT3 narrow body front wheels with 245/35-19 tires.
If your objective is to fix the tucked-in look of the OEM RS Spyder wheels, you'll have to go with either GT3RS wheels or aftermarket wheels that have more aggressive offsets. Simply going with a 325 rear tire won't do it. Here is mine with GT3RS rear wheels and 325/30-19 tires, and GT3 narrow body front wheels with 245/35-19 tires.
Exactly. My 2011 GTS came with 325 rears and they did nothing for the overall stance. If anything they made it look worse since the diameter was greater than 305's so it sort of made the rear of the car look raised. May be other options available now. But like you say, the only real solution for centerlock wheels is after market wheels with custom offsets or GT3RS wheels like the ones you have. Looks really good.