Apparently this is not possible using managed code at this time. PInvoke is the only option currenlty. I used PInvoke.User32 nuget package.

Use AppWindow class from Windows App SDK

// Retrieve the window handle (HWND) of the current (XAML) WinUI 3 window.
IntPtr hWnd = WinRT.Interop.WindowNative.GetWindowHandle(this);

// Retrieve the WindowId that corresponds to hWnd.
WindowId windowId = Win32Interop.GetWindowIdFromWindow(hWnd);

// Lastly, retrieve the AppWindow for the current (XAML) WinUI 3 window.
AppWindow appWindow = AppWindow.GetFromWindowId(windowId);
appWindow.Closing += AppWindow_Closing;

private void AppWindow_Closing(AppWindow sender, AppWindowClosingEventArgs args)
{
    args.Cancel = true;
}

https://docs.microsoft.com/en-us/windows/apps/windows-app-sdk/windowing/windowing-overview

Here is my implementation based on the PInvoke.User32 nuget package.

Version using Window parameter

    public void MaximizeWindow(Window window)
    {
        var windowHandle = WinRT.Interop.WindowNative.GetWindowHandle(window);

        PInvoke.User32.ShowWindow(windowHandle, PInvoke.User32.WindowShowStyle.SW_MAXIMIZE);
    }

Version using extension method

This previous code can also be transformed into an extension method for the Window class, so I can just call this.Maximize() from within the Window:

public static class WindowExtensions
{
    public static void Maximize(this Window window)
    {
        var windowHandle = WinRT.Interop.WindowNative.GetWindowHandle(window);

        PInvoke.User32.ShowWindow(windowHandle, PInvoke.User32.WindowShowStyle.SW_MAXIMIZE);
    }
}

Usage in your Window derived class:

this.Maximize();

Minize and Restore

The "PInvoke.User32.WindowShowStyle" definition used in the examples above contains also constants for SW_MINIMIZE and SW_RESTORE, but I did not test this.