How to bend a specific part of an object or differently achieve a bend/round surface this is actually my first post on the Blender StackExchange so I hope I ask my question properly^^.

I am rather new to Blender and currently trying to model a Desert Eagle. It's going good so far, just started it 2 hours ago but now I ran into a problem. I am trying to make the red marked piece of the gun but I have actually no Idea how to properly get this bend surface. I thought about using a Deform Modifier, but as the whole green marked part is one object it would bend the whole object, which I obviously don't want. Sculpting isnt really an option for me as I want to keep it as low poly as possible additionally I have no clue how sculpting works, actually never used it. Is there any option to get it close to the picture? I doesn't have to be perfectly round but I cannot manage to even get close to a rounded surface.

Thanks to all of you in advance :)
As your base shape is a cylinder you could begin with a cylinder and use the Boolean modifier to cut off the parts you're talking about, then continue to model, create some edge loops, use the knife, and at the end add some bevels to sharp the edges: