mouse_event / PostMessage key down messages - inconsistent with GetKeyState() - windows

Question

I'm trying to do two things:
Send "key down" events, both for keyboard keys, as well as mouse keys, to an external process' window
Later on, query whether a given keyboard or mouse key is currently pressed in that window, which could happen if
My tool had previously sent a "key down" (but obviously no key up) event to the window
The user had any manual interaction with the window
One of the cases could for example be that I send a "key down" event for the left mouse button to the window. The user then clicks inside the window themselves manually. As a consequence after both of those interactions, the window recognizes the mouse key as "up" again.
So far, for the key presses, I've been using user32.dll API calls PostMessage (for keyboard events) and mouse_event (for mouse keys).
As for retrieving the current state, I've been trying to use "GetKeyState". However, its return values are inconcistent with actual behaviour. For example, when I post a key down through my tool, and there are no further interactions (neither by me, nor by the user), GetKeyState() still returns 0 (= key is NOT pressed).
I presume I'm using the wrong API for retrieving the state here (in particular as GetKeyState doesn't take in a window handle either?).
Is there any way to figure out the actual key state for the given window? Or am I going wrong elsewhere here?
Thanks
Example code:
class NativeCalls
{
[DllImport("user32.dll", SetLastError = true)]
public static extern bool PostMessage(IntPtr hWnd, uint Msg, int wParam, int lParam);
[DllImport("user32.dll")]
public static extern short GetKeyState(int nVirtKey);
[DllImport("user32.dll")]
public static extern bool SetForegroundWindow(IntPtr hWnd);
[DllImport("user32.dll")]
static extern short GetAsyncKeyState(int vKey);
public static void test()
{
var state_x1 = GetAsyncKeyState(0x41);
var ok1 = SetForegroundWindow(Globals.Hwnd);
var ok2 = PostMessage(Globals.Hwnd, 0x0100, 0x41, 0); // key down "A"
Thread.Sleep(10);
var state = GetKeyState(0x41); // check if key "A" Is down
var state_x2 = GetAsyncKeyState(0x41);
// state_x1, state, and state_x2 are all 0
}
}