I just had three jugs delivered and pulled one off the shelf at Walmart. Have not had a problem getting QS Euro 5W-40 in the last 5 years or so using it.
The PCV valves are known for not lasting very long in the EA888, I used to replace mine at around 40k intervals as maintenance. Not extremely expensive and easy to replace. I'd start there.
If you log a bunch of bone stock vehicles you will see 2-3 degrees of knock retard quite a bit, especially FI cars. Thankfully, a KR gauge is not a factory option otherwise we would have a forum called bobistheknockguy.com.
Unfortunately the BRZ does not offer temp reading in digits but a graph which gives you a rough idea. In roughly 80 degrees at Thunder Hill I would run 20 minute sessions without any concern of oil temps without a cooler. I run advanced group for reference.
How about lifters? Same opinion as for the bearings?
What is your go to oil weight for a SBC which would see some additional heat and load over a daily driven vehicle?
If you are at 1k miles now I would watch the oil level and not baby it. If you have manual mode occasionally decelerate using engine braking. My hunch is consumption will decrease.