From the Github README:

Also, for the very first time, introducing tiny11 core builder! A more powerful script, designed for a quick and dirty development testbed. Just the bare minimun, none of the fluff. This script generates a significantly reduced Windows 11 image. However, it's not suitable for regular use due to its lack of serviceability - you can't add languages, updates, or features post-creation. tiny11 Core is not a full Windows 11 substitute but a rapid testing or development tool, potentially useful for VM environments.

It literally says that it cannot be updated from a built OS install. You need to reinstall tiny11 by rebuilding the install image with a newer Windows 11 base image. Obviously it would be best to do this every time there is a security patch release for Windows 11.

EDIT: Rereading further, the bigger Tiny11 image might be able to be updated in-OS. I'm going to dig through the ps1 scripts to see if the README holds up to that un-noted capability.

EDIT2: I don't see any registry edits that knock Windows Updater offline. I'll test it in a VM to see if things work (from prebuilt when it eventually downloads). Though I am unsure at this moment if such an image's changes will survive a Windows update at all.

EDIT3: VM not tested yet, but an issue on the GitHub seems to corroborate my initial assumption.

EDIT4: VM tested. Things claimed to be patched out (Edge) came back with one of the cumulative updates applied shortly after install. Other cumulative updates are being blocked (error instantly on attempt to install after download) (perhaps unintentionally). Image downloaded claimed to be for 23H2, but Windows 11 22H2 was installed, seemingly with no way to actually upgrade. I think my point stands.