You are kind of wrong, in that the effect of the extra muscle is pretty minimal. See this video on the topic:

What about muscles? Muscles burn 3 times more calories at rest than fat. This sounds impressive, but tissues like your brain, skin or intestines burn way more. In absolute terms, a more muscular body composition makes a difference for how many calories your body burns, but it’s relatively small. Muscles matter a lot for health, longevity and performance, but not that much for weight loss.

https://www.youtube.com/watch?v=vSSkDos2hzo

What you learn quickly is that the effects of calorie burning are real but way less than what people think. You can go destroy yourself running to the point you're half dead and that's gonna burn like 300 calories (like, one protein bar).

But yes on topic of the gym there's a few downstream effects, the bigger you get the more you eat to be on equilibrium. Also strength workouts keep your muscles "activated" for up to 48h during which you also burn a bit more calories at rest.

And finally of course there's the whole bulking/cutting thing, the basics is that basically, no matter how much you lift you're not gonna grow muscle unless you also have a calorie surplus in particular protein. During this process it's unavoidable to also put on fat so you bulk for a while (eat a lot+ workout a lot and improve personal records) then you cut (eat at deficit, maintenance workouts) so the fat recedes and etc.

There's a saying among body builders. Abs are made in the kitchen.

You get strength in the gym.

By that logic a morbidly obese person is exercising harder than anyone else by moving their 600lb ass around the living room.