We can use a hidden func XInputGetCapabilitiesEx from XInput 1.4 (comes with Windows 8) to fetch gamepad VID/PID

XInputGetCapabilitiesEx.cpp

typedef struct _XINPUT_CAPABILITIES_EX
{
	XINPUT_CAPABILITIES Capabilities;
	WORD VendorId;
	WORD ProductId;
	WORD VersionNumber;
	WORD unk1;
	DWORD unk2;
} XINPUT_CAPABILITIES_EX, *PXINPUT_CAPABILITIES_EX;

// XInputGetCapabilitiesEx hidden function is available since Windows 8 version of XInput1_4.dll
DWORD XInputGetCapabilitiesEx(DWORD dwUserIndex, PXINPUT_CAPABILITIES_EX pCapabilitiesEx)
{
	DWORD(WINAPI* XInputGetCapabilitiesExFunc)(DWORD unk1, DWORD dwUserIndex, DWORD dwFlags, PXINPUT_CAPABILITIES_EX pCapabilities);
	XInputGetCapabilitiesExFunc = reinterpret_cast<decltype(XInputGetCapabilitiesExFunc)>(::GetProcAddress(::GetModuleHandleW(L"XInput1_4.dll"), (LPCSTR)108));

	if (!XInputGetCapabilitiesExFunc)
		return ERROR_INVALID_FUNCTION;

	return XInputGetCapabilitiesExFunc(1, dwUserIndex, 0, pCapabilitiesEx);
}

....
XINPUT_CAPABILITIES_EX caps {};

XInputGetCapabilitiesEx(m_UserIndex, &caps);

// Fixup for Wireless Xbox 360 Controller
if (caps.ProductId == 0 && caps.Capabilities.Flags & /*XINPUT_CAPS_WIRELESS*/0x0002)
{
	caps.VendorId = 0x045E;
	caps.ProductId = 0x02A1;
}

m_VendorId = caps.VendorId;
m_ProductId = caps.ProductId;

// Known controller VID/PID list: https://github.com/libsdl-org/SDL/blob/main/src/joystick/controller_type.c