Set immersion style at runtime

Yes it is possible using the immersionStyle method.

Here's a snippet to illustrate this:

import SwiftUI

@main
struct DynamicImmersionApp: App {
    
    @Environment(\.openImmersiveSpace) var openImmersiveSpace
    @Environment(\.dismissImmersiveSpace) var dismissImmersiveSpace
    
    @State private var immersionStyle:ImmersionStyle = .mixed
    @State private var showImmersiveSpace = false

    var body: some SwiftUI.Scene {
        WindowGroup {
            VStack {
                if showImmersiveSpace {
                    Button("Dismiss immersion") {
                        showImmersiveSpace = false
                    }
                }
                else {
                    Button("Show mixed immersion") {
                        immersionStyle = .mixed
                        showImmersiveSpace = true
                    }
                    
                    Button("Show full immersion") {
                        immersionStyle = .full
                        showImmersiveSpace = true
                    }
                }
            }
            .onChange(of: showImmersiveSpace) { _, newValue in
                Task {
                    // simplified for brevity
                    print(newValue)
                    if newValue {
                        await openImmersiveSpace(id: "ImmersiveSpace")
                    } else {
                        await dismissImmersiveSpace()
                    }
                }
            }
        }
        
        ImmersiveSpace(id: "ImmersiveSpace") {
            ImmersiveView()
        }.immersionStyle(selection: .constant(immersionStyle), in: immersionStyle)
    }
}