If you view the table you can see that muscle tissue is slightly more metabolically active than adipose tissue. However, it’s not by much.
Adding 1lb of muscle mass doesn’t burn an extra 50 cal per day. We’d be looking at adding around 8lbs of muscle tissue for a 48kcal increase on our BMR (on average, yo). How many calories per day a person burns at rest (BMR) is largely determined by the size of the human, regardless of body composition. If weight loss is undertaken then naturally BMR will climb down as there is simply less of a person at the end of the weight loss phase (assuming it was successful). Don’t overcomplicate this stuff.
Similarly BMR will go up if a person gains mass, be that muscle or body fat because there is more tissue to power now. More energy is needed to keep the lights on.
Realistically the main way to make an impact on TDEE (total daily energy expenditure, which is the sum of BMR and activity + other bits) is to become more active.
Activity doesn’t just include grinding through workouts in the gym. Walking is an underrated activity that’s free, accessible to most and generally enjoyable. Also you can see dogs.
If you use your muscles via resistance training they will require energy for repair, combine that with being a human with a step count and your TDEE may reach places it’s never been before.
Table is the accurate to latest revision of the work of Elia, 1992. Wang, Z., Ying, Z., Bosy-Westphal, A., Zhang, J., Heller, M., Later, W., Heymsfield, S. and Müller, M. (2011). Evaluation of specific metabolic rates of major organs and tissues: Comparison between men and women.