Updating KMS to activate Server 2022?

KMS is running on Server 2016, and currently can activate up to Server 2019.
When I try to add the Server 2022 key from the link below, it says "Unable to verify product key The specified product key is invalid, or is unsupported on the version of VAMT. An update to support additional products may be available online."
Ok, no problem, there's a "Check for updates online" link. However that throws a 404 error.

I tried this: https://learn.microsoft.com/en-us/windows-server/get-started/kms-client-activation-keys which produces the error "Code: 0xC004E016. The Software Licensing Service reported that the product key is invalid."
It seems obvious that this is the correct action, because keys from that page for other Server activation levels, are already in the VAMT 'Product Keys' list.

I've seen some old posts saying that an update to at least an ADK version 10.1.9.XXXXX is needed.
Can anyone confirm that?

Also I'm having a hard time triangulating what my "Server 2022 KMS host key" actually is.
For configuring online activation, is it only the keys in the article above?

We also recently had to move from an EA to MPSA licensing scheme, so there have been backend changes to our Microsoft contract in the last month.

Thanks