I think that’s self explanatory, why does load factor (G) affect stall speed? Why does load factor result reaching the critical angle of attack at higher airspeed?
What does 'having' a load factor1 mean? It means, by definition, that you are experiencing a force G times your weight. It doesn't matter how it happens: in a turn or loop or turbulence. But in all cases practically all that force (which usually counteracts the weight) comes from lift.
In normal unaccelerated flight, lift = weight. In a more general case, lift = weight $\times$ G. If G > 1, you need more lift than weight.2
How can you get more lift (from the same wing)? Either you go faster, or you increase angle of attack. So inevitably, for a given speed, you'll have to fly at a higher angle of attack, closer to stall. Or in other words, you'll reach stall at a higher speed than normal.
Note that exactly the same thing happens if you 'just' increase your weight, by other means than transient loading with G - say, by having more cargo or fuel. Again, you'll need more lift - with exactly the same consequences.
1 Load factor is applicable in all three axes, but we are implicitly talking about the normal factor in relation to stall speed. When you are accelerating forward or skidding, you'll also have a load factor, but it'll usually be well below 1.0.
2 On the other hand, if G = 0, you don't need wings at all and you'll go ballistic.
The forces on an aircraft in straight and level unaccelerated flight must equal. The horizontal force of lift and centrifugal force (load) must equal. The vertical force of lift and weight (load) must equal. Thrust and drag must equal. At a steady airspeed, increasing weight (load) must have a corresponding increase in lift. To increase lift without changing configuration, you have to increase the angle of attack of the flight surfaces. The same happens when you bank the plane in a turn. Just the degree of force acting in each direction changes.
Total lift and induced drag are both a factor of airspeed and angle of attack. The higher the airspeed, the more lift you have. The higher the angle of attack, the more lift you have. If you have a constant amount of lift, airspeed and angle of attack become inversely proportionate.
If you are in a coordinated turn, you are dividing your total lift between horizontal and vertical components. The horizontal component works against centrifugal force in a turn. The vertical component is therefore reduced to be less than your weight. To stay at a constant altitude, you have to increase the angle of attack by pulling back on the yoke (and trim). The pitching action will increase the load factor.