Yes, sustained turns are mainly influenced by those two. If an aircraft's altitude and speed are stable, it means the
vertical component of the lift matches its weight and its thrust matches the drag. And the
lateral component of lift is what turns the aircraft.
The formula for lift is 1/2 * coefficient of lift * air density * lifting area * velocity^2. An oversized wing means a smaller coefficient of lift is needed which means the aircraft would need a smaller angle of attack while turning. This is important because the coefficient of drag does not increase together with the coefficient of lift as the AoA increases. Airfoils tend to have an optimum point below 10 degrees. Anything above 15 degrees tends to be very inefficient. An example:
View attachment 144418
The goal with the 4th gens was having them efficient while pulling high G forces. They were very draggy while cruising but they had much less drag than the 3rd gens while pulling, let's say, 6 Gs. The third gens needed massive control surface deflections and an AoA near their stall points to generate such lifts. The 4th gens didn't.
A higher thrust helps the sustained turn performance from the other side. It allows the aircraft to be draggier while turning. Everything same, an aircraft with higher thrust would be able to use a higher AoA without losing energy. Thrust to weight ratio is actually not a great representation for this unless one is comparing aircraft of the similar size. Heavier aircraft need less of it because the surface area increases slower than the mass (scaling law). The J-36 having a TWR around 1 at its weight is quite huge.