STRATEGIES TO COMPENSATE FOR DEFICITS BETWEEN THE SAME MUSCLES ON BOTH SIDES OF THE BODY.
ANSWER

The problem cannot be solved in a complex way. However, the weak muscle can be brought into line with the stronger one. However, the fact that the weak muscle will always lag behind the strong one is and remains a fact that we must learn to live with.
IS IT POSSIBLE TO BUILD MUSCLE AND LOSE FAT AT THE SAME TIME?
However, I have most of the equipment at home (barbell, dumbbells, flat bench, pull-up bar and a Kettler all-round device). I would be happy if you could create a split training program and a nutrition plan for me, as I haven't found the optimum yet.
ANSWER
Because your weight is relatively low for your size, I recommend that you first go through a bulking phase with the goal of increasing muscle mass. The body burns significantly more fat when there is more active (muscle) mass available. It will therefore be easier for you to lose fat after the bulking phase than if you start a diet now with little muscle mass.
When building muscle, stick to a diet rich in protein and carbohydrates with a moderate fat content. Many of my columns have covered this topic in great detail, so it's worth reading up on them. When training, I recommend a four-way split - this way you train the entire body once a week. You should reduce your endurance training a little during this phase so that you don't burn too many of the calories needed for building muscle. Twice 20 to 30 minutes a week with a pulse of around 150 beats per minute will boost the cardiovascular system and keep your metabolism "on the go". A comprehensive training and nutrition plan would unfortunately go beyond the scope of this column. But you will find a lot of valuable information on this website.