So I figured I'd share my experience here. I run a different tire size set than normal which mean my tire pressure is generally lower than OEM specs. Unfortunately the "proper" pressure for my rears is very close to the TPMS's cutoff so when temps started to drop the TPMS went off, this annoyed me for 2 weeks because even when temps picked back up and the pressure was correct the damn TPMS holds onto the alert unless you bring the pressure over what it expects so i had to over inflate my rear tires by roughly 9psi for a bit to clear the TPMS and my god the car handled like shit during this period.
Super twitchy on the highway and more oversteer as well. This probably would have been great for AutoX but not for a long highway stint. When I got to my destination and the light cleared I brought the rears back down to the proper pressure and the car returned to it's more stable attitude as before.
TLDR: Maybe try checking your tire pressures and lower it in the rear a bit and see if that helps at all. Tire pressure is often overlooked but has a big impact on how a car handles.