How to scale a SwiftUI view to fit its parent

Code that reproduces the issue

import SwiftUI

@main
struct KeyboardLayoutProblemApp: App {
    var body: some Scene {
        WindowGroup {
					iOSTabView()
        }
    }
}

struct iOSTabView: View {
	var body: some View {
		TabView {
			GameView()
				.frame(maxWidth: UIScreen.main.bounds.width, maxHeight: UIScreen.main.bounds.height)
				.tabItem {
					Label("Play", systemImage: "gamecontroller.fill")
				}
		}
	}
}

struct GameView: View {
	var body: some View {
		VStack {
			Text("Play")
			Spacer()
			KeyboardView()
		}
		.padding()
	}
}

struct KeyboardView: View {	
	let firstRowLetters = "qwertyuiop".map { $0 }
	let secondRowLetters = "asdfghjkl".map { $0 }
	let thirdRowLetters = "zxcvbnm".map { $0 }
	
	var body: some View {
		VStack {
			HStack {
				ForEach(firstRowLetters, id: \.self) {
					LetterKeyView(character: $0)
				}
			}
			HStack {
				ForEach(secondRowLetters, id: \.self) {
					LetterKeyView(character: $0)
				}
			}
			HStack {
				ForEach(thirdRowLetters, id: \.self) {
					LetterKeyView(character: $0)
				}
			}
		}
		.padding()
	}
}

struct LetterKeyView: View {
	let character: Character
	
	var width: CGFloat { height*0.8 }
	@ScaledMetric(relativeTo: .title3) private var height = 35
	
	var body: some View {
		Button {
			print("\(character) pressed")
		} label: {
			Text(String(character).capitalized)
				.font(.title3)
				.frame(width: self.width, height: self.height)
				.background {
					RoundedRectangle(cornerRadius: min(width, height)/4, style: .continuous)
						.stroke(.gray)
				}
		}
		.buttonStyle(PlainButtonStyle())
	}
}

Problem

GameView doesn't fit its parent view:

Question

How do I make GameView be at most as big as its parent view?

What I've tried and didn't work

GameView()
  .frame(maxWidth: .infinity, maxHeight: .infinity)

GeometryReader { geometry in
  GameView()
    .frame(maxWidth: geometry.size.width, maxHeight: geometry.size.height)
}

GameView()
  .clipped()

GameView()
  .layoutPriority(1)

GameView()
  .scaledToFit()

GameView()
  .minimumScaleFactor(0.01)

GameView()
  .scaledToFill()
  .minimumScaleFactor(0.5)

I'm not using UIScreen.main.bounds.width because I'm trying to build a multi-platform app.