Recomp is possible. But it's more so depending on if you're at a certain stage with your lifting, I believe. If you're still in a newbie phase, then yes you could lose fat and gain muscle at the same time. But if you are an advanced athlete, you really have to choose one or the other.
Now can you lose fat and gain strength at the same time? Yes. But losing fat and gaining muscle isn't really viable if you're multiple years into your lifting journey. If you eat at maintenance, nothing will really change. If you eat in a surplus, you will gain muscle with some fat and if you eat in a deficit, you will lose fat and won't really be gaining muscle.
So if you're a newbie, I would approach it by eating at maintenance or in a surplus (depending on overall body fat %), whereas for a more advanced lifter, I would pick one or the other to get the best results.
Hope that helps!
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