Alfa's page for the AWUS036NHA says the chipset is the Atheros AR9271. The AR 9271 data sheet has a PROMISCUOUS bit in the receive filter register, described as "Promiscuous receive enable; Enable reception of all frames, including errors", which sounds like monitor mode.
And, in fact, the Linux ath9k driver turns that bit on for monitor mode.
On Windows, however, it's not clear whether "promiscuous" mode, as opposed to monitor mode, is supported on 802.11 adapters. To quote the page for the OID_GEN_CURRENT_PACKET_FILTER OID:
Note When the miniport driver is in Native 802.11 modes other than NetMon, and OID_GEN_CURRENT_PACKET_FILTER is set, the driver must not fail the set request if any promiscuous or raw filter settings are enabled in the OID data.
However, Guidelines for 802.11 Promiscuous Receive Operations says:
Note It is only valid for the miniport driver to enable the NDIS_PACKET_TYPE_PROMISCUOUS, NDIS_PACKET_TYPE_802_11_PROMISCUOUS_MGMT, or NDIS_PACKET_TYPE_802_11_PROMISCUOUS_CTRL packet filters if the driver is operating in Network Monitor (NetMon) or Extensible Access Point (AP) modes.
So they're saying both "the driver must allow NDIS_PACKET_TYPE_PROMISCUOUS to be set in modes other than NetMon mode" and "NDIS_PACKET_TYPE_PROMISCUOUS is only valid in NetMon and AP modes". I have some vague memory that the first of those used to say "must fail the request" rather than "must not fail the request", which would be more consistent with the second of those.
So it may be that promiscuous mode, in the NDIS_PACKET_TYPE_PROMISCUOUS sense, doesn't work on 802.11 adapters unless you're in monitor mode. That's the mode that's used by WinPcap and Npcap if a caller turns on "promiscuous mode" (it's the correct mode to use for Ethernet adapters), so turning on "promiscuous mode" in sniffers using libpcap/WinPcap/Npcap, such as Wireshark, may not work for 802.11 adapters.
Now why monitor mode isn't working is another matter. WinPcap doesn't support monitor mode; if you have WinPcap installed, un-install it, and install Npcap. This wiki page says it may or may not work, depending on the Windows version and the driver. (I think there's an error with the "Firmware/Driver version" and "Windows version" columns, where some of the items have the values swapped - including the Alfa item.)
Presumably some documentation says it's capable of promiscuous mode. What does the documentation say promiscuous mode (promiscuous mode, not monitor mode) means for that adapter?
It's advertised as an adapter for promiscuous, monitor (rfmon), and packet injection. It is the highest recommended card I could find, and reviews are all great. It is an Alfa Awus036nha if you want to see if you can find any additional info. Thanks