Sometimes you just have shitty workouts, it happens to all of us.
I had mine yesterday…
I started of with high bar back squat and this time I had my favorite pink flat shoes on.
My angle on my torso was more forward due to my long thighs and short chins(lower leg)
My knees needs to come forward a bit more to help me keep my torso more upright which will also give me a slight different angle.
It was a lot harder,I was not as focused as I should be,plus I did not felt that much in my quadriceps because of this and it felt like I was just doing my rep without thinking and full control.
Last time (and several of weeks back) I have been using other shoes for squat with a bit thicker heal,it is like when you place something under your heal when you squat to keep your torso more upright.
That worked a lot better for me especially with my body structure.
So yes! Shoes does matter.
If you change shoes often, then you might feel that you are stronger one week and not as strong the next week (with the same exercise for lower body)if you change shoes, and that has to do with the angle and stress it put on your muscles.