How do you eat to gain muscle and lose fat?

Hallu.

I started my own business about 3 years ago, and since then I've been sitting around more than usual. I actually always weighed around 100 kilos, which at 180 cm is already a belly and overweight, but according to the BMI only the lowest threshold of obesity.
Well, I haven't weighed in ages, simply because I didn't have a scale. I have now done that, however, and have reached a proud 120 kilos.

I wanted to start changing my free time now because I originally spent it in my armchair in front of the laptop after work.
The thing is, however, that training without the right nutrition may not do anything.
Now on the one hand I came across low carb with a calorie deficit,
and on the other hand I read that you need a calorie excess of approx. 300-500 kcal for muscle building where carbohydrates should cover 50% of the daily energy intake, especially before and after training.

My question is now. What is the best way to do it?
I tend to train with high intensity every other day to promote regeneration. Do I just eat low carb on a rest day and still have excess calories, while on training days I treat myself to a few oatmeal and a banana?
Can I burn fat and build muscle at the same time despite excess calories with training and proper nutrition?
I don't want to have a hyper athletic body now, but I think a little muscle mass is more handsome than just losing 30 kilos.

Securing energy through carbohydrates in training sounds obvious, because it is simply the lighter source of energy, while the body at Lowcarb burns fat in order to stay alive, since carbohydrates are avoided.

Unfortunately, I find nothing about this mix of losing weight and building muscle. Therefore, I would also be happy about experiences and the certainty that I can drive a surplus with dietary changes and training, and still lose fat.

He does it like this: