(Usual disclaimer: please note that I'm just another Forum user here, I'm NOT an Ubuntu Developer and/or Ubuntu MATE Developer).
As far as I can tell, you're absolutely right, unfortunately: the "Alt + Windows key + S" key (also known as "Alt + Super + S") key combination / shortcut is not working, in the logon screen, to launch the Orca Screen Reader in "Ubuntu MATE 22.04". At least, it's not working for me in my laptop computer that I upgraded from Ubuntu MATE 20.04.5 LTS ("Focal Fossa") to Ubuntu MATE 22.04.1 LTS ("Jammy Jellyfish") about two months ago.
I've found the following directly related bug, reported by @Norbert_X in Launchpad, on 9th April 2021 (2021-04-09), for Ubuntu MATE 20.10 and 21.04:
A few minutes ago, I've marked that bug as also affecting me and I've added the following comment in that bug web page:
I'm guessing that it may be a good idea to also open an "Issue" in the "Issues"page of the "arctica-greeter" repository in "GitHub":
I hope this reply of mine was useful, in some way.
Following up to my previous reply in this same Topic / Discussion: I've opened, a few minutes ago, the following "Issue" in the "arctica-greeter" Issues page in the "GitHub" repository. Let's see if I get a reply.