How can I get the size of the monitor that my current window is on in WinUI 3 and Win32?

I have an HWND window in my app, and I want to know the size of the monitor it's on. This will help me position my HWND on the monitor in some scenarios.

How can I get the resolution of the monitor for a given window/HWND in WinUI 3 and Win32 (in C++, preferrably)?

Once you have an HWND for your window (for example, see Retrieve a window handle (HWND) for WinUI 3, WPF, and WinForms), you can use Win32 functions for this:

// Get the HWND, for clarity
HWND GetHwndForWindow(winrt::Window const& window)
{
    auto nativeWindow = window.try_as<::IWindowNative>();
    HWND hwnd{};
    winrt::check_hresult(nativeWindow->get_WindowHandle(&hwnd));
    return hwnd;
}

// See note below about "work area"
RECT GetMonitorWorkAreaForWindow(winrt::Window const& window)
{
    const auto hwnd = GetHwndForWindow(window);

    // https://learn.microsoft.com/en-us/windows/win32/api/winuser/nf-winuser-monitorfromwindow
    const auto hmonitor = ::MonitorFromWindow(hwnd, MONITOR_DEFAULTTONEAREST);

    // https://learn.microsoft.com/en-us/windows/win32/api/winuser/nf-winuser-getmonitorinfoa
    MONITORINFO monitorInfo{sizeof(MONITORINFO)};
    THROW_IF_WIN32_BOOL_FALSE(GetMonitorInfo(hmonitor, &monitorInfo));
    return monitorInfo.rcWork;
}

If you're looking for usable space, you probably want the work area, and not the actual size of the monitor (rcWork, not rcMonitor). See the Taskbar#Taskbar Display Options and MONITORINFO.

See MonitorFromWindow and GetMonitorInfo.