If you don't want an actual chroot jail, then you would have to isolate the user's sessions into a separate mount namespace, then have
/var/test bind mounted onto
/root within that namespace only. Achieving that would require customization of the user session creation. Perhaps a custom PAM library could do it?
(Implementation left as an exercise for the reader: I actually don't know of any ready-made tools suitable for implementing this, so this might require programming a custom PAM library. However, the containerization technology has caused a lot of fast development on Linux namespaces - perhaps there actually is something usable for this already implemented, and I just don't know about it?)
However: if I encountered a system where a non-root user like
test123 had write access to
/root, let alone had it as a home directory, I would immediately assume some sort of trickery, as that would be an extremely abnormal and insecure configuration if real. If I noticed this and had no root access, I'd try and notify the actual sysadmin ASAP. If I was the sysadmin and had no other explanation, I'd strongly prefer to disconnect this system from the network (first taking forensic memory dumps if possible), shut it down and take its disk(s) to another computer for analysis, which would defeat your deception as a side effect.
So I don't really see what might be achievable with this set-up, other than an exercise in diagnostics & forensics.