Front squats are more taxing in terms of your ability to keep your thoracic spine/upper back from collapsing than anything else, where as pretty much all barbell based squats are going to require some sort of core stability. Depending on how you back squat that might be a reason, might have lost some quad strength as with fronties you always have to be getting your hips back under the bar on the way up and keeping tension on the quads or you drop the bar where as you can get away with more lean with other variations/less quads. Might be down to an overall reduction in squatting volume. Hard to tell.
There are some squat variations that the Smith is somewhat okay for; if there's no hack squat machine for instance you can do these which are pretty much the equivalent and take advantage of the unnautral ROM of the machine to target the quads. It's only for secondary work though, RIP if no actual rack.
I feel like my weakness during squats is my upper back colapsing so ill try the smith machine front squats.
Although I agree with your last sentance, I think I can manage without the power rack if I can deadlift and squat in my normal gym on the weekend
Did you continue training with the pain or take time off? Deadlifts / Squats / Barbell Rows seem okay (not sure about Press yet)