How to correctly implement a connection between different views for general object changes

I get to change the color on one view, when I switch, the standard is restored in the next view

Sorry, I cannot reproduce the issue, using the code fragments shown, filling many missing parts by guess.
(I needed to change one "Black" to another value to test with, but that is the only change I made.)

In my opinion, you should better use @EnvironmentObject, but @ObservedObject works quite well if you pass the instance correctly.

Can you show the whole code of the project which can reproduce the issue?

@Tact,

There wasn't much provided except for a few pieces of code, so it is hard to determine the exact flow of your application, so I took some liberty in piecing together what you might have. I have also never tried to implement this style of application, so I decided to try my best to solve it; learned some new things! Below is what I got working:

Code Block 
class Store: ObservableObject {
    @Published var backgroundColor: Color
    init() {
        self.backgroundColor = .green
    }
}
struct ChangeBackgroundColor: View {
    @Binding var backgroundColor: Color
    var body: some View {
        ZStack {
            VStack {
                Button(action: { self.backgroundColor = .black }, label: { Text("Black") })
                Button(action: { self.backgroundColor = .green }, label: { Text("Green") })
            }
        }
        .frame(minWidth: 0, maxWidth: .infinity, minHeight: 0, maxHeight: .infinity)
        .background(backgroundColor).edgesIgnoringSafeArea(.all)
    }
}
struct ContentView: View {
    @ObservedObject var store: Store = Store()
    var body: some View {
        NavigationView {
            VStack {
                NavigationLink(destination: ChangeBackgroundColor(backgroundColor: $store.backgroundColor)) {
                    Text("Pick Background Color")
                }
            }
            .frame(minWidth: 0, maxWidth: .infinity, minHeight: 0, maxHeight: .infinity)
            .background(store.backgroundColor).edgesIgnoringSafeArea(.all)
        }
    }
}

I ran into the issue that others have encountered when trying to set the background color that involves the NavigationView. It appears that the the underline View either doesn't have/use the dimensions of the screen, so either using GeometryReader or .infinity should get a desired effect of turning the whole background color via just SwiftUI. Hopefully this will get you going and understand the relationship on how to pass values around different views.

If you don't plan on using NavigationView or some of the other views that have issues with .background, you can easily use Color() example you provided.

@ OOper

Here is my test project
My Test Project

The structure may not be correct, but I'm still learning)

@Tylor
Thanks for your code, I will try to adapt it!