Huh. I was just reading the release notes for the just-released Ubuntu MATE 24.10, when I came across the following which sounds surprisingly similar to what you're experiencing:
Switched back to Slick Greeter (replacing Arctica Greeter) due to race-condition in the boot process which results the display manager failing to initialise.
I dunno. Maybe you could try installing the Slick Greeter on your Ubuntu MATE 24.04 and see if the autologin works there? 