OSK

Osk.cs

public static class Osk
{
    public static void Show()
    {
        if (InputPane.IsClosed())
            TabTip.Toggle();
    }

    public static void Hide()
    {
        if (!InputPane.IsClosed())
            TabTip.Toggle();
    }
}

// https://stackoverflow.com/a/40921638
public static class TabTip
{
    public static void Toggle()
    {
        var uiHostNoLaunch = new UIHostNoLaunch();
        var tipInvocation = (ITipInvocation)uiHostNoLaunch;
        tipInvocation.Toggle(GetDesktopWindow());
        Marshal.ReleaseComObject(uiHostNoLaunch);
    }

    [ComImport, Guid("4ce576fa-83dc-4F88-951c-9d0782b4e376")]
    class UIHostNoLaunch
    {
    }

    [ComImport, Guid("37c994e7-432b-4834-a2f7-dce1f13b834b")]
    [InterfaceType(ComInterfaceType.InterfaceIsIUnknown)]
    interface ITipInvocation
    {
        void Toggle(IntPtr hwnd);
    }

    [DllImport("user32.dll", SetLastError = false)]
    static extern IntPtr GetDesktopWindow();
}

// https://stackoverflow.com/a/55513524
public static class InputPane
{
    [ComImport, Guid("D5120AA3-46BA-44C5-822D-CA8092C1FC72")]
    public class FrameworkInputPane
    {
    }

    [ComImport, SuppressUnmanagedCodeSecurity,
     InterfaceType(ComInterfaceType.InterfaceIsIUnknown),
     Guid("5752238B-24F0-495A-82F1-2FD593056796")]
    public interface IFrameworkInputPane
    {
        [PreserveSig]
        int Advise(
            [MarshalAs(UnmanagedType.IUnknown)] object pWindow,
            [MarshalAs(UnmanagedType.IUnknown)] object pHandler,
            out int pdwCookie
        );

        [PreserveSig]
        int AdviseWithHWND(
            IntPtr hwnd,
            [MarshalAs(UnmanagedType.IUnknown)] object pHandler,
            out int pdwCookie
        );

        [PreserveSig]
        int Unadvise(
            int pdwCookie
        );

        [PreserveSig]
        int Location(
            out Rectangle prcInputPaneScreenLocation
        );
    }

    public static bool IsClosed()
    {
        var inputPane = (IFrameworkInputPane)new FrameworkInputPane();
        inputPane.Location(out var rect);
        Marshal.ReleaseComObject(inputPane);

        return rect is { Width: 0, Height: 0 };
    }
}

Enable Show touch keyboard button at system try.
When there is a device (capable of touch input), this gist works, otherwise, one has to click the systray keyboard button to create an instance, from then on, it works.