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One of the things that catches most people off guard when they start exercising: how much stronger they are one side versus the other. Stronger left leg or stronger right arm or shoulder etc.
You can really feel this when you do pull ups, bicep curls, dumbbell shoulder presses, single leg squats etc. While using a barbell or bilateral patterns, you can mask this deficit.
But the deficit can never be fully erased. It is an accumulation of tens of thousands of activity and movement choices you make over the years. Pick a bag, jump over a puddle, carrying a bag, carrying a baby, pushing harder with one leg while climbing the stairs.
And these asymmetries are amplified when we exercise. When we exert ourselves, we will resort to using our dominant side and muscles that are stronger to get the job done.
It takes a great deal of monitoring and cognisance to even be aware that this is happening. And even then, you can manage this by overcompensating or being mindful. But you will always favour one side.
Take a pull up I attempted with an unconventional grip. My palms are prone. And my shoulders rolled back. But my right side is having an easier time pulling my weight to the bar. This is natural given I am right-side dominant. My right arm is stronger. As is the right side of my body in general. So I try to compensate with a little more effort on the left side. And I keep an eye on my form through videos to see if my intent translates into quality execution and less pronounced asymmetries.
Now, the logical question should be: is it worth worrying about this so much? After all, you are going to always favour one side.
I think it is worth your consideration. Exercise and training are thoughtful activity choices that compensate for inactivity and underuse of muscles and different joint groups. Part of that dysfunction is our tendency to favour one side. So I try. Even when I know it will never be the same.