Calorie tracking and restriction pretty much comes with strict keto. Transitioning to keto rigorously requires detailed tracking of every molecule that goes in your mouth (with a food scale and measuring cups), at least for the first 12 weeks. I tracked constantly for about 6 mos until it was automatic for me and I knew every food and portion I typically encounter at a glance. It's hard at first but only tracking part way is the #1 reason for failing to get results.
I didn't do any exercise at all while losing weight, in fact while changing diet I was more sedentary than my usual slug-like activity level due to work and life factors. For me, exercise has always been hard, unpleasant and inevitably makes me hungrier. N=1 but that's what worked best for me and my weight loss was dramatic and super fast (>100 lbs in 8 mos).